Summer School & Conference Schedule
|
|
|
- Job Newton
- 5 years ago
- Views:
Transcription
1 Summer School & Conference Schedule Valuation Theory and Integral Closures in Commutative Algebra JULY 3 22, 2006 UNIVERSITY OF OTTAWA (Lectures on Valuation Theory) Lecturers: F.V. Kuhlmann, D. Cutkosky, H. Knaf, B. Teissier, M. Vaquié. (Lectures on Integral Closures) Lecturers: I. Swanson, W. Bruns, A. Taylor. Chapter and section numbers refer to the book Integral closure of ideals, rings, and modules by Irena Swanson and Craig Huneke. Relevant chapters will be distributed during the summer school by permission of the publisher. Lectures will be held in SITE C0136 at the south end of campus for the first two weeks, and in SITE B0138 during the third week. Week 1 (Summer School) Monday Tuesday Wednesday Thursday Friday 9:30 10:30 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture Lecture 2 Lecture 2 Lecture 2 Lecture 2 Lecture Lunch Lunch Lunch Lunch Lunch 2 3 Lecture 3 Lecture 3 Lecture 3 Lecture 3 Lecture 3 3:30 4:30 Lecture 4 Lecture 4 Lecture 4 Lecture 4 Lecture 4 Evening Discussions/ Discussions/ Discussions/ Discussions/ Discussions/ Problems Problems Problems Problems Problems Monday July 3 Lecture 1 (Kuhlmann & Knaf): Valuations, value groups and valuation rings (6.1, 6.2) Lecture 2 (Kuhlmann & Knaf): Properties of valuation rings (6.4) Lecture 3 (Swanson): What is integral closure of ideals (1.1 (lightly), 1.2) Lecture 4 (Swanson): Integral closure of rings (2.1, 2.2 lightly) Tuesday July 4 Lecture 1 (Kuhlmann & Knaf): Existence of valuation rings; completions, (6.3, 6.5) 1
2 Lecture 2 (Kuhlmann & Knaf): Valuation theoretical invariants (6.6) Lecture 3 (Swanson): Noetherian questions (4.3.4, 4.6) Lecture 4 (Swanson): Valuative criterion (6.8) Wednesday July 5 Lecture 1 (Kuhlmann & Knaf): Examples of valuations (6.7) Lecture 2 (Kuhlmann & Knaf): Extensions of valuations, fundamental inequality Lectures 3 and 4 (Swanson): Rees valuations (10.1, 10.2, 10.4) Thursday July 6 Lecture 1 (Kuhlmann & Knaf): Defect, with examples, and defectless valuations Lecture 2 (Kuhlmann & Knaf): Ramification theory, I Lecture 3 (Swanson): Monomial ideals (integral closure, Newton polyhedra, Rees valuations) Lecture 4 (Swanson): Two-dimensional regular local rings: Zariski s theory and Rees valuations Friday July 7 Lecture 1 (Kuhlmann & Knaf): Ramification theory, II Lecture 2 (Kuhlmann & Knaf): Hensel s Lemma and Implicit Function Theorem Lecture 3 (Swanson): Divisorial valuations (9.3) Lecture 4 (Swanson): Reductions and Rees valuations (10.5) Saturday July 8 Catch-up Week 2 (Summer School) Monday Tuesday Wednesday Thursday Friday 8:30 9:30 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture Lecture 2 Lecture 2 Lecture 2 Lecture 2 Lecture :45 Lunch Lunch Lunch Lunch Lunch 12:45 1:45 Lecture 3 Lecture 3 Lecture 3 Lecture 3 Lecture 3 2 3:30 Lab Lab Lab Lab Lab 4 5 Lecture 4 Lecture 4 Lecture 4 Lecture 4 Evening Discussions/ Discussions/ Discussions/ Discussions/ Problems Problems Problems Problems 2
3 Monday July 10 Lecture 1 (Kuhlmann): Elimination of ramification I: the generalized stability theorem Lecture 2 (Swanson): Jacobian criteria, Serre s criteria Lecture 3 (Amelia Taylor): General normalization algorithms Lab (Amelia Taylor): Introduction to some symbolic computer algebra packages Lecture 4 (Knaf) Local uniformization of Abhyankar places in arbitrary characteristic Tuesday July 11 Lecture 1 (Kuhlmann): Elimination of ramification II: henselian rationality Lecture 2 (Knaf) Ideas towards general local uniformization Lecture 3 (Swanson): Computing Rees valuations Lab (Amelia Taylor): Computing Rees valuations Lecture 4 (Winfried Bruns): Polyhedral geometry Wednesday July 12 Lecture 1 (Vaquié): Extension of a valuation: key-polynomial and augmented valuation Lecture 2 (Cutkosky): geometric theory of local rings, I Lecture 3 and Lab (Amelia Taylor): Vasconcelos s algorithms Lecture 4 (Winfried Bruns): Affine monoid rings and their normalizations Thursday July 13 Lecture 1 (Vaquié): Extension of a valuation: admissible family and defect Lecture 2 (Teissier): Local uniformization in characteristic p, I Lecture 3 (Winfried Bruns): Algorithms for normalizations of affine monoid rings Lab (Winfried Bruns): Normaliz Friday July 14 Lecture 1 (Vaquié): Graded algebra associated to a valuation of K[x] Lecture 2 (Teissier): Local uniformization in characteristic p, II Lecture 3 (Swanson): Noether normalizations Lab (Taylor): Lecture 4 (Swanson): Ad hoc methods for computing integral closure Saturday July 15 Catch-up 3
4 Week 3 (Conference) Monday Tuesday Wednesday Thursday Friday Saturday July 17 July 18 July 19 July 20 July 21 July :45 Cutkosky I Brenner Goto Gaffney Vasconcelos 10 10:45 Cutkosky II Ghezzi Hübl Campillo Huneke 11 11:30 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break 11:30 12 Kashcheyeva Naghipour Järvilehto Bivià-Ausina Rond 12 2 Lunch Lunch Lunch Lunch Lunch 2 2:45 Knaf Villarreal Abhyankar Spivakovsky 3 3:45 Kuhlmann Vituli Schoutens Vaquié 4 4:30 Coffee Break Coffee Break Coffee Break 4:30 5:15 Teissier I Brennan Teissier II Titles: 7 Conference Dinner 1. Shreeram Abhyankar: Some Thoughts on the Jacobian Conjecture 2. Carles Bivià-Ausina: Mixed multiplicities of ideals and the Milnor number of an isolated complete intersection singularity 3. Joseph P. Brennan: Sequences that preserve homological degree 4. Holger Brenner: Grothendieck topologies and ideal closure operations - The integral closure and the submersive topology 5. Antonio Campillo: Complete ideals and Poincaré series 6. Cutkosky (I): Geometric theory of local rings, II 7. Cutkosky (II): Geometric theory of local rings, III 8. Terence Gaffney: Pairs of modules, equisingularity, and the multiplicity-polar theorem 4
5 9. Laura Ghezzi: Monomialization of generating sequences of valuations in two dimensional function fields 10. Shiro Goto: The Cohen-Macaulayness in the graded rings G(I) = n 0 I n /I n+1 associated to ideals I = Q : m Reinhold Hübl: Adjoints of Ideals and Rees Valuations 12. Craig Huneke: Absolute Integral Closure 13. Tarmo Järvilehto: Jumping numbers of a simple complete ideal in a two dimensional regular local ring 14. Olga Kashcheyeva: Jumping polynomials in 2-dimensional regular local rings 15. Hagen Knaf: Local uniformization after finite extension of the function field 16. F.-V. Kuhlmann: Classification of Artin-Schreier defect extensions 17. Reza Naghipour: Local cohomology and quintasymptotic primes of ideals with respect to modules 18. Guillaume Rond: Artin strong approximation theorem 19. Hans Schoutens: Valuations on Noetherian rings via Grassmanian paths 20. Mark Spivakovsky: Kaplansky s theorem on generalized power series and local uniformization in arbitrary characteristic 21. Bernard Teissier (I): Local uniformization in characteristic p, III 22. Bernard Teissier (II): TBA 23. Michel Vaquié: Extension of a valuation, Newton polygon 24. Wolmer V. Vasconcelos: Complexity Topics in the Normalization of Algebras 25. Rafael H. Villarreal: Blowup algebras and subrings associated to monomial ideals 26. Marie A. Vitulli: Weak subintegral closure of ideals and connections with reductions and valuations 5
M ath. Res. Lett. 15 (2008), no. 2, c International Press 2008 JOINT REDUCTIONS OF MONOMIAL IDEALS AND MULTIPLICITY OF COMPLEX ANALYTIC MAPS
M ath. Res. Lett. 15 (2008), no. 2, 389 407 c International Press 2008 JOINT REDUCTIONS OF MONOMIAL IDEALS AND MULTIPLICITY OF COMPLEX ANALYTIC MAPS Carles Bivià-Ausina Abstract. We characterize the joint
Extended Index. 89f depth (of a prime ideal) 121f Artin-Rees Lemma. 107f descending chain condition 74f Artinian module
Extended Index cokernel 19f for Atiyah and MacDonald's Introduction to Commutative Algebra colon operator 8f Key: comaximal ideals 7f - listings ending in f give the page where the term is defined commutative
IDEALS AND THEIR INTEGRAL CLOSURE
IDEALS AND THEIR INTEGRAL CLOSURE ALBERTO CORSO (joint work with C. Huneke and W.V. Vasconcelos) Department of Mathematics Purdue University West Lafayette, 47907 San Diego January 8, 1997 1 SETTING Let
LOCAL COHOMOLOGY IN COMMUTATIVE ALGEBRA AND ALGEBRAIC GEOMETRY
LOCAL COHOMOLOGY IN COMMUTATIVE ALGEBRA AND ALGEBRAIC GEOMETRY POSTER ABSTRACTS Presenter: Eric Canton Title: Asymptotic invariants of ideal sequences in positive characteristic via Berkovich spaces Abstract:
VALUATION SEMIGROUPS OF NOETHIERIAN LOCAL DOMAINS
VALUATION SEMIGROUPS OF NOETHIERIAN LOCAL DOMAINS STEVEN DALE CUTKOSKY 1. Introduction Suppose that (R, m R ) is a Noetherian local domain, with quotient field K, and ν is a valuation of K which dominates
Preliminary Exam Topics Sarah Mayes
Preliminary Exam Topics Sarah Mayes 1. Sheaves Definition of a sheaf Definition of stalks of a sheaf Definition and universal property of sheaf associated to a presheaf [Hartshorne, II.1.2] Definition
Integral closures of ideals and rings
Integral closures of ideals and rings Irena Swanson ICTP, Trieste School on Local Rings and Local Study of Algebraic Varieties 31 May 4 June 2010 I assume some background from Atiyah MacDonald [2] (especially
GROWTH OF RANK 1 VALUATION SEMIGROUPS
GROWTH OF RANK 1 VALUATION SEMIGROUPS STEVEN DALE CUTKOSKY, KIA DALILI AND OLGA KASHCHEYEVA Let (R, m R ) be a local domain, with quotient field K. Suppose that ν is a valuation of K with valuation ring
arxiv:math/ v1 [math.ac] 11 Nov 2005
![arxiv:math/ v1 [math.ac] 11 Nov 2005](/thumbs/93/111611618.jpg "arxiv:math/ v1 [math.ac] 11 Nov 2005")
A note on Rees algebras and the MFMC property arxiv:math/0511307v1 [math.ac] 11 Nov 2005 Isidoro Gitler, Carlos E. Valencia and Rafael H. Villarreal 1 Departamento de Matemáticas Centro de Investigación
arxiv: v3 [math.ac] 3 Jul 2012
![arxiv: v3 [math.ac] 3 Jul 2012](/thumbs/94/121630641.jpg "arxiv: v3 [math.ac] 3 Jul 2012")
DAGGER CLOSURE IN REGULAR RINGS CONTAINING A FIELD HOLGER BRENNER AND AXEL STÄBLER arxiv:1103.1786v3 [math.ac] 3 Jul 2012 Abstract. We prove that dagger closure is trivial in regular domains containing
Overweight deformations of affine toric varieties and local uniformization
Overweight deformations of affine toric varieties and local uniformization Bernard Teissier To the memory of Shreeram S. Abhyankar Abstract. A valuation of a local domain (R, m) is the datum of a valuation
Adjoints of ideals. Reinhold Hübl and Irena Swanson
Adjoints of ideals Reinhold Hübl and Irena Swanson Abstract. We characterize ideals whose adjoints are determined by their Rees valuations. We generalize the notion of a regular system of parameters, and
The analogue of Izumi s Theorem for Abhyankar valuations
Submitted exclusively to the London Mathematical Society doi:10.1112/0000/000000 The analogue of Izumi s Theorem for Abhyankar valuations by G. Rond and M. Spivakovsky Dedicated to the memory of Shreeram
Commutative Algebra: Connections with Algebraic Topology and Representation Theory May 18-22, 2008 University of Nebraska-Lincoln.
Commutative Algebra: Connections with Algebraic Topology and Representation Theory May 18-22, 2008 University of Nebraska-Lincoln Talk Abstracts Speaker: Dave Benson Title: Squeezed resolutions and the
arxiv: v2 [math.ag] 3 May 2018
![arxiv: v2 [math.ag] 3 May 2018](/thumbs/80/80549161.jpg "arxiv: v2 [math.ag] 3 May 2018")
EXTENSIONS OF VALUATIONS TO THE HENSELIZATION AND COMPLETION arxiv:171208562v2 [mathag] 3 May 2018 STEVEN DALE CUTKOSKY 1 Introduction Suppose that K is a field Associated to a valuation ν of K is a value
Resolution of Singularities. Steven Dale Cutkosky. Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Resolution of Singularities Steven Dale Cutkosky Department of Mathematics, University of Missouri, Columbia, Missouri 65211 To Hema, Ashok and Maya Contents Preface vii Chapter 1. Introduction 1 1.1.
ALGORITHMS FOR ALGEBRAIC CURVES
ALGORITHMS FOR ALGEBRAIC CURVES SUMMARY OF LECTURE 7 I consider the problem of computing in Pic 0 (X) where X is a curve (absolutely integral, projective, smooth) over a field K. Typically K is a finite
DESCENT OF THE CANONICAL MODULE IN RINGS WITH THE APPROXIMATION PROPERTY
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 124, Number 6, June 1996 DESCENT OF THE CANONICAL MODULE IN RINGS WITH THE APPROXIMATION PROPERTY CHRISTEL ROTTHAUS (Communicated by Wolmer V. Vasconcelos)
Modules, ideals and their. Rees algebras
Modules, ideals and their Rees algebras Santiago Zarzuela University of Barcelona Conference on Commutative, Combinatorial and Computational Algebra In Honour to Pilar Pisón-Casares Sevilla, February 11-16,
Intersecting valuation rings in the Zariski-Riemann space of a field
Intersecting valuation rings in the Zariski-Riemann space of a field Bruce Olberding Department of Mathematical Sciences New Mexico State University November, 2015 Motivation from Birational Algebra Problem:
Inseparable local uniformization. Conference on valuation theory, El Escorial
Inseparable local uniformization M. Temkin July 27, 2011 Conference on valuation theory, El Escorial Outline 1 General paradigm of desingularization The state of the art Main result of the talk Generalizations
MASTERCLASS MARCH 2013 BY Ben Elias, MIT, Boston and Geordie Williamson, MPI, Bonn Titel: Soergel bimodules & Kazhdan-Lusztig conjectures
Venue: aud. G1 Monday 18 March, The Cast 10.00-10.45 Introduction: Category O and the Kazhdan-Lusztig conjectures The happenings of 1979. The miracle of KL polynomials. Arbitrary Coxeter groups. The miracle
Integral Closure of Ideals, Rings, and Modules
London Mathematical Society Lecture Note Series 336 Integral Closure of Ideals, Rings, and Modules Irena Swanson and Craig Huneke Cambridge University Press London Mathematical Society Lecture Note Series
Additive Polynomials over Perfect Fields
Additive Polynomials over Perfect Fields Salih Durhan Abstract. Additive polynomials in one variable over valued fields of positive characteristic are sufficiently well understood in terms of their approximation
AN INEQUALITY INVOLVING TIGHT CLOSURE AND PARAMETER IDEALS. Dedicated to the memory of Professor Nicolae Radu
AN INEQUALITY INVOLVING TIGHT CLOSURE AND PARAMETER IDEALS CĂTĂLIN CIUPERCĂ AND FLORIAN ENESCU Dedicated to the memory of Professor Nicolae Radu ABSTRACT. We establish an inequality involving colengths
MIT Algebraic techniques and semidefinite optimization February 16, Lecture 4
MIT 6.972 Algebraic techniques and semidefinite optimization February 16, 2006 Lecture 4 Lecturer: Pablo A. Parrilo Scribe: Pablo A. Parrilo In this lecture we will review some basic elements of abstract
Arithmetic vs. Geometric results in char. 0
Arithmetic vs. Geometric results in char. 0 Griff Elder May 27 31, 2013 Setting Let p be prime and Q p be the p-adic numbers. Elements of Q p look like Laurent series in p: 1 a t p t + + a 1 1 p + a 0
Extending valuations to formal completions.
Extending valuations to formal completions F J errera Govantes Departamento de Álgebra Facultad de Matemáticas Avda Reina Mercedes, s/n Universidad de Sevilla 41012 Sevilla, Spain email: jherrera@algebrauses
Errata and Minor Additions for Integral Closure of Ideals, Rings, and Modules by Irena Swanson and Craig Huneke
Errata and Minor Additions for Integral Closure of Ideals, Rings, and Modules by Irena Swanson and Craig Huneke These errata pages are based on observations by many people. We thank Rüdiger Achilles, Carles
m-full AND BASICALLY FULL IDEALS IN RINGS OF CHARACTERISTIC p
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 44, Number 2, 2014 m-full AND BASICALLY FULL IDEALS IN RINGS OF CHARACTERISTIC p JANET C. VASSILEV ABSTRACT. We generalize the notion of m-full and basically
COURSE SUMMARY FOR MATH 508, WINTER QUARTER 2017: ADVANCED COMMUTATIVE ALGEBRA
COURSE SUMMARY FOR MATH 508, WINTER QUARTER 2017: ADVANCED COMMUTATIVE ALGEBRA JAROD ALPER WEEK 1, JAN 4, 6: DIMENSION Lecture 1: Introduction to dimension. Define Krull dimension of a ring A. Discuss
A GENERALIZATION OF THE AUSLANDER-NAGATA PURITY THEOREM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 127, Number 1, January 1999, Pages 71 78 S 0002-9939(99)04501-3 A GENERALIZATION OF THE AUSLANDER-NAGATA PURITY THEOREM MIRIAM RUTH KANTOROVITZ (Communicated
arxiv:math/ v2 [math.ac] 9 Mar 2007
![arxiv:math/ v2 [math.ac] 9 Mar 2007](/thumbs/93/112554269.jpg "arxiv:math/ v2 [math.ac] 9 Mar 2007")
A note on Rees algebras and the MFMC property arxiv:math/0511307v2 [math.ac] 9 Mar 2007 Isidoro Gitler 1, Carlos E. Valencia and Rafael H. Villarreal Departamento de Matemáticas Centro de Investigación
Matrix Factorizations. Complete Intersections
Matrix Factorizations for Complete Intersections Irena Peeva (Cornell University) Linear Algebra: Vector Spaces finite dimensional over a Field e.g. C tool: basis Algebra: Modules finitely generated over
THE ALGEBRA AND MODEL THEORY OF TAME VALUED FIELDS
THE ALGEBRA AND MODEL THEORY OF TAME VALUED FIELDS FRANZ VIKTOR KUHLMANN Abstract. A henselian valued field K is called a tame field if its algebraic closure K is a tame extension, that is, the ramification
On the vanishing of Tor of the absolute integral closure
On the vanishing of Tor of the absolute integral closure Hans Schoutens Department of Mathematics NYC College of Technology City University of New York NY, NY 11201 (USA) Abstract Let R be an excellent
MATH 131B: ALGEBRA II PART B: COMMUTATIVE ALGEBRA
MATH 131B: ALGEBRA II PART B: COMMUTATIVE ALGEBRA I want to cover Chapters VIII,IX,X,XII. But it is a lot of material. Here is a list of some of the particular topics that I will try to cover. Maybe I
ABSTRACT NONSINGULAR CURVES
ABSTRACT NONSINGULAR CURVES Affine Varieties Notation. Let k be a field, such as the rational numbers Q or the complex numbers C. We call affine n-space the collection A n k of points P = a 1, a,..., a
THE ALGEBRA AND MODEL THEORY OF TAME VALUED FIELDS
THE ALGEBRA AND MODEL THEORY OF TAME VALUED FIELDS FRANZ VIKTOR KUHLMANN Abstract. A henselian valued field K is called a tame field if its algebraic closure K is a tame extension, that is, the ramification
arxiv: v2 [math.ac] 7 Nov 2017
![arxiv: v2 [math.ac] 7 Nov 2017](/thumbs/89/99379957.jpg "arxiv: v2 [math.ac] 7 Nov 2017")
SYMBOLIC BLOWUP ALGEBAS OF MONOMIAL CUVES IN A 3 DEFINED BY AIHMEIC SEQUENCE CLAE D CUZ arxiv:1708.01374v [math.ac] 7 Nov 017 Abstract. In this paper, we consider monomial curves ina 3 k parameterized
The structure of spaces of valuations and the local uniformization problem
The structure of spaces of valuations and the local uniformization problem A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the degree of
Math 711: Lecture of September 7, Symbolic powers
Math 711: Lecture of September 7, 2007 Symbolic powers We want to make a number of comments about the behavior of symbolic powers of prime ideals in Noetherian rings, and to give at least one example of
m-full AND BASICALLY FULL IDEALS IN RINGS OF CHARACTERISTIC p
m-full AND BASICALLY FULL IDEALS IN RINGS OF CHARACTERISTIC p JANET C. VASSILEV Abstract. We generalize the notion of m- full and basically full ideals in the setting of tight closure and demonstrate some
Characteristic p methods in characteristic zero via ultraproducts
Characteristic p methods in characteristic zero via ultraproducts Hans Schoutens Abstract In recent decades, by exploiting the algebraic properties of the Frobenius in positive characteristic, many so-called
arxiv: v1 [math.ac] 23 Jun 2010
![arxiv: v1 [math.ac] 23 Jun 2010](/thumbs/94/118299368.jpg "arxiv: v1 [math.ac] 23 Jun 2010")
INDICES OF NORMALIZATION OF IDEALS arxiv:1006.4560v1 [math.ac] 23 Jun 2010 C. POLINI, B. ULRICH, W. V. VASCONCELOS, AND R. VILLARREAL Abstract. We derive numerical estimates controlling the intertwined
REDUCTION NUMBERS OF EQUIMULTIPLE IDEALS
REDUCTION NUMBERS OF EQUIMULTIPLE IDEALS CĂTĂLIN CIUPERCĂ Abstract. Let (A, m) be an unmixed local ring containing a field. If J is an m-primary ideal with Hilbert-Samuel multiplicity e A (J), a recent
Algebraic Geometry and Convex Geometry. A. Khovanskii
Algebraic Geometry and Convex Geometry A. Khovanskii 1 Intersection index on an irreducible variety X, dim X = n Let K(X) be the semigroup of spaces L of rational functions on X such that: a) dim L
Newton filtrations, graded algebras and codimension of non-degenerate ideals
CADERNOS DE MATEMÁTICA 02, 15 38 March (2001) ARTIGO NÚMERO SMA#89 Newton filtrations, graded algebras and codimension of non-degenerate ideals Carles Bivià-Ausina * Departament de Geometria i Topologia,
arxiv: v2 [math.ac] 7 Mar 2018
![arxiv: v2 [math.ac] 7 Mar 2018](/thumbs/93/113410879.jpg "arxiv: v2 [math.ac] 7 Mar 2018")
MAXIMAL COHEN-MACAULAY MODULES OVER CERTAIN SEGRE PRODUCTS LINQUAN MA arxiv:1802.04786v2 [math.ac] 7 Mar 2018 Dedicated to Professor Gennady Lyubeznik on the occasion of his 60th birthday Abstract. We
Krull Dimension and Going-Down in Fixed Rings
David Dobbs Jay Shapiro April 19, 2006 Basics R will always be a commutative ring and G a group of (ring) automorphisms of R. We let R G denote the fixed ring, that is, Thus R G is a subring of R R G =
Notes Friday, September 09, 2016
Notes Friday, September 09, 2016 Day 1 - Polynomials Page 1 Notes Friday, September 09, 2016 Day 1 - Polynomials Page 2 Notes Friday, September 09, 2016 Day 1 - Polynomials Page 3 Notes Friday, September
Primary Decompositions of Powers of Ideals. Irena Swanson
Primary Decompositions of Powers of Ideals Irena Swanson 2 Department of Mathematics, University of Michigan Ann Arbor, Michigan 48109-1003, USA iswanson@math.lsa.umich.edu 1 Abstract Let R be a Noetherian
THE SMOOTH BASE CHANGE THEOREM
THE SMOOTH BASE CHANGE THEOREM AARON LANDESMAN CONTENTS 1. Introduction 2 1.1. Statement of the smooth base change theorem 2 1.2. Topological smooth base change 4 1.3. A useful case of smooth base change
Jacobian Conjecture: A Birational Geometry Approach
Jacobian Conjecture: A Birational Geometry Approach Alexander Borisov University of Pittsburgh March 5, 2013 Johns Hopkins University Algebraic Geometry and Number Theory Seminar 1 Suppose n N. Suppose
Hilbert Functions of Filtered Modules
Maria Evelina Rossi, Giuseppe Valla Hilbert Functions of Filtered Modules April 20, 2010 Springer Preface Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming
Gröbner Complexes and Tropical Bases
Gröbner Complexes and Tropical Bases Jan Verschelde University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science http://www.math.uic.edu/ jan jan@math.uic.edu Graduate
QUALIFYING EXAMINATION Harvard University Department of Mathematics Tuesday 10 February 2004 (Day 1)
Tuesday 10 February 2004 (Day 1) 1a. Prove the following theorem of Banach and Saks: Theorem. Given in L 2 a sequence {f n } which weakly converges to 0, we can select a subsequence {f nk } such that the
H.6 Homological Characterization of Rings: The Commutative Case
The Concise Handbook of Algebra, Kluwer Publ. (2002), 505-508 H.6 Homological Characterization of Rings: The Commutative Case Sarah Glaz glaz@uconnvm.uconn.edu A large number of niteness properties of
Resolution of Singularities in Algebraic Varieties
Resolution of Singularities in Algebraic Varieties Emma Whitten Summer 28 Introduction Recall that algebraic geometry is the study of objects which are or locally resemble solution sets of polynomial equations.
THE ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES OVER RINGS OF SMALL DIMENSION. Thomas Marley
THE ASSOCATED PRMES OF LOCAL COHOMOLOGY MODULES OVER RNGS OF SMALL DMENSON Thomas Marley Abstract. Let R be a commutative Noetherian local ring of dimension d, an ideal of R, and M a finitely generated
Constructible Invariants
Constructible Invariants Hans Schoutens Department of Mathematics City University of New York 365 Fifth Avenue New York, NY 10016 (USA) Abstract A local numerical invariant is a map ω which assigns to
On seminormal monoid rings
Journal of Algebra 302 (2006) 361 386 www.elsevier.com/locate/jalgebra On seminormal monoid rings Winfried Bruns a,, Ping Li b, Tim Römer a a FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück,
ELIMINATION OF RAMIFICATION II: HENSELIAN RATIONALITY
ELIMINATION OF RAMIFICATION II: HENSELIAN RATIONALITY FRANZ-VIKTOR KUHLMANN Abstract. We prove in arbitrary characteristic that an immediate valued algebraic function field F of transcendence degree 1
RESEARCH STATEMENT JANET VASSILEV
RESEARCH STATEMENT JANET VASSILEV My research lies in the realm of commutative ring theory. One of my interests is to study new algebraic structures determined by various closure operations. I am also
PRIMARY DECOMPOSITION OF MODULES
PRIMARY DECOMPOSITION OF MODULES SUDHIR R. GHORPADE AND JUGAL K. VERMA Department of Mathematics, Indian Institute of Technology, Mumbai 400 076, India E-Mail: {srg, jkv}@math.iitb.ac.in Abstract. Basics
Equimultiplicity and Blowing up An Algebraic Study
M. Herrmann S. Ikeda U. Orbanz Equimultiplicity and Blowing up An Algebraic Study With an Appendix by B. Moonen Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Manfred Herrmann Ulrich Orbanz
ON SEMINORMAL MONOID RINGS
ON SEMINORMAL MONOID RINGS WINFRIED BRUNS, PING LI, AND TIM RÖMER ABSTRACT. Given a seminormal affine monoid M we consider several monoid properties of M and their connections to ring properties of the
INTERSECTION THEORY CLASS 2
INTERSECTION THEORY CLASS 2 RAVI VAKIL CONTENTS 1. Last day 1 2. Zeros and poles 2 3. The Chow group 4 4. Proper pushforwards 4 The webpage http://math.stanford.edu/ vakil/245/ is up, and has last day
Tropical Varieties. Jan Verschelde
Tropical Varieties Jan Verschelde University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science http://www.math.uic.edu/ jan jan@math.uic.edu Graduate Computational Algebraic
Introduction to Quadratic Forms over Fields
Introduction to Quadratic Forms over Fields T.Y. Lam Graduate Studies in Mathematics Volume 67.. American Mathematical Society 1 " " M Providence, Rhode Island Preface xi ; Notes to the Reader xvii Partial
How Teissier mixed multiplicities
Université de Lille 1, France Conference Singular Landscapes Aussois, France The 22-nd of June 2015 Bernard Teissier s wisdom Better a house without roof than a house without view. Hunza saying (starting
Castelnuovo-Mumford Regularity and finiteness of Hilbert Functions
Castelnuovo-Mumford Regularity and finiteness of Hilbert Functions Maria Evelina Rossi, Department of Mathematics, University of Genoa, Via Dodecaneso 35, 16146 Genoa, Italy E-mail: rossim@dimaunigeit
Weak Normality and Seminormality
Weak Normality and Seminormality Marie A. Vitulli Abstract In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties
arxiv: v1 [cs.it] 26 Apr 2007
![arxiv: v1 [cs.it] 26 Apr 2007](/thumbs/83/88084802.jpg "arxiv: v1 [cs.it] 26 Apr 2007")
EVALUATION CODES DEFINED BY PLANE VALUATIONS AT INFINITY C. GALINDO AND F. MONSERRAT arxiv:0704.3536v1 [cs.it] 26 Apr 2007 Abstract. We introduce the concept of δ-sequence. A δ-sequence generates a wellordered
ALGEBRAIC GEOMETRY COURSE NOTES, LECTURE 9: SCHEMES AND THEIR MODULES.
ALGEBRAIC GEOMETRY COURSE NOTES, LECTURE 9: SCHEMES AND THEIR MODULES. ANDREW SALCH 1. Affine schemes. About notation: I am in the habit of writing f (U) instead of f 1 (U) for the preimage of a subset
On the Cancellation Problem for the Affine Space A 3 in characteristic p
On the Cancellation Problem for the Affine Space A 3 in characteristic p Neena Gupta School of Mathematics, Tata Institute of Fundamental Research Dr. Homi Bhabha Road, Colaba, Mumbai 400005, India e-mail
1.1. Important observations. The set
Composition algebras over local fields revisited Holger P. Petersson Fakultät für Mathematik und Informatik FernUniversität in Hagen D-58084 Hagen Germany Email: holger.petersson@fernuni-hagen.de Workshop
A criterion for p-henselianity in characteristic p
A criterion for p-henselianity in characteristic p Zoé Chatzidakis and Milan Perera Abstract Let p be a prime. In this paper we give a proof of the following result: A valued field (K, v) of characteristic
APPLICATIONS OF LOCAL COHOMOLOGY
APPLICATIONS OF LOCAL COHOMOLOGY TAKUMI MURAYAMA Abstract. Local cohomology was discovered in the 960s as a tool to study sheaves and their cohomology in algebraic geometry, but have since seen wide use
REGULAR CLOSURE MOIRA A. MCDERMOTT. (Communicated by Wolmer V. Vasconcelos)
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 127, Number 7, Pages 1975 1979 S 0002-9939(99)04756-5 Article electronically published on March 17, 1999 REGULAR CLOSURE MOIRA A. MCDERMOTT (Communicated
Resolving singularities of plane analytic branches with one toric morphism
Resolving singularities of plane analytic branches with one toric morphism Rebecca Goldin and Bernard Teissier To Heisuke Hironaka Abstract Let (C, 0) be an irreducible germ of complex plane curve. Let
Eureka Math Module 4 Topic G Solving Equations
Eureka Math Module 4 Topic G Solving Equations Lessons 23-27 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make
FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASSES 47 AND 48
FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASSES 47 AND 48 RAVI VAKIL CONTENTS 1. The local criterion for flatness 1 2. Base-point-free, ample, very ample 2 3. Every ample on a proper has a tensor power that
Qualifying Exam Syllabus. I. Algebraic Geometry (Major - Algebra)
Qualifying Exam Syllabus Ritvik Ramkumar November 29, 2017, 9:00am, Evans 891 Committee: David Eisenbud (Advisor), Martin Olsson, Denis Auroux (Chair), Marjorie Shapiro (External) 1. Scheme Theory I. Algebraic
Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples Oct. 17, William Heinzer Christel Rotthaus Sylvia Wiegand
Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples Oct. 17, 2017 William Heinzer Christel Rotthaus Sylvia Wiegand Department of Mathematics, Purdue University, West Lafayette,
On the Abhyankar-Moh inequality
On the Abhyankar-Moh inequality Evelia García Barroso La Laguna University, Tenerife September, 2014 In this talk we present some results of R.D. Barrolleta, E. García Barroso and A. Płoski, On the Abhyankar-Moh
CHARACTERISTIC p METHODS AND TIGHT CLOSURE
CHARACTERISTIC p METHODS AND TIGHT CLOSURE ANURAG K. SINGH These are the notes of four lectures given at the Abdus Salam International Centre for Theoretical Physics, Trieste, in June 2004 on tight closure
Vector bundles and ideal closure operations
Commutative Algebra and Noncommutative Algebraic Geometry, I MSRI Publications Volume 67, 2015 Vector bundles and ideal closure operations HOLGER BRENNER This is an introduction to the use of vector bundle
TOPOLOGIES ON SPACES OF VALUATIONS: A CLOSENESS CRITERION. 1. Introduction
TOPOLOGIES ON SPACES OF VALUATIONS: A CLOSENESS CRITERION JOSNEI NOVACOSKI Abstract. This paper is part of a program to understand topologies on spaces of valuations. We fix an ordered abelian group Γ
DUALITY FOR KOSZUL HOMOLOGY OVER GORENSTEIN RINGS
DUALITY FO KOSZUL HOMOLOGY OVE GOENSTEIN INGS CLAUDIA MILLE, HAMIDEZA AHMATI, AND JANET STIULI Abstract. We study Koszul homology over Gorenstein rings. If an ideal is strongly Cohen-Macaulay, the Koszul
Enumeration of Concave Integer Partitions
3 47 6 3 Journal of Integer Sequences, Vol. 7 (004), Article 04..3 Enumeration of Concave Integer Partitions Jan Snellman and Michael Paulsen Department of Mathematics Stockholm University SE-069 Stockholm,
BOUNDS IN POLYNOMIAL RINGS OVER ARTINIAN LOCAL RINGS
BOUNDS IN POLYNOMIAL RINGS OVER ARTINIAN LOCAL RINGS HANS SCHOUTENS ABSTRACT. Let R be a (mixed characteristic) Artinian local ring of length l and let X be an n-tuple of variables. This paper provides
Syllabuses for Honor Courses. Algebra I & II
Syllabuses for Honor Courses Algebra I & II Algebra is a fundamental part of the language of mathematics. Algebraic methods are used in all areas of mathematics. We will fully develop all the key concepts.
MA 252 notes: Commutative algebra
MA 252 notes: Commutative algebra (Distilled from [Atiyah-MacDonald]) Dan Abramovich Brown University April 1, 2017 Abramovich MA 252 notes: Commutative algebra 1 / 21 The Poincaré series of a graded module
Algebraic groups Lecture 1
Algebraic groups Lecture Notes by Tobias Magnusson Lecturer: WG September 3, 207 Administration Registration: A sheet of paper (for registration) was passed around. The lecturers will alternate between
arxiv: v1 [math.ac] 24 Feb 2010
![arxiv: v1 [math.ac] 24 Feb 2010](/thumbs/93/112519701.jpg "arxiv: v1 [math.ac] 24 Feb 2010")
ON THE DEPTH OF BLOW-UP INGS OF IDEALS OF MINIMAL MIXED MULTIPLICITY arxiv:1002.4466v1 [math.ac] 24 Feb 2010 CLAE D CUZ Abstract. We show that if (,m) is a Cohen-Macaulay local ring and I is an ideal of
Commutative Algebra and Algebraic Geometry
Commutative Algebra and Algebraic Geometry Lecture Notes Johannes Kepler Universität Linz Summer 2018 Prof. Franz Winkler c Copyright by F. Winkler Contents References 1. Introduction....................................................................1
A study of irreducible polynomials over henselian valued fields via distinguished pairs
A study of irreducible polynomials over henselian valued fields via distinguished pairs Kamal Aghigh, Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran aghigh@kntu.ac.ir, Anuj