D (X) D,o(X) Db(~) Db /~ r m1(-filp) A A~ Aa Aa,AM BG. Db(x) D+(X) D<-b(X),D>-~(X) mi(x) Df Dx D D+(XIY) D~(XIY) D~(X,,S)

Transcription

1 Bibliography. [BBD] A.Beilinson, J.Bernstein, P.Deligne. Faiceaux perverse, Asterisque, [Bol] A.Borel et al.. Intersection cohomology, Birkhauser, [Bo2] A.Borel et al.. Algebraic D-modules, Academic Press, [Boil] A.Borel. Sur la cohomologie des espaces fibres prineipaux et des espaces homogenes de group de Lie compacts, Ann. Math., 7 (193), [D1] P.Deligne. Theorie de Hodge III, Publ. Math. IHES. 44 (1974), -78. [D2] P.Deligne. La conjecture de Weil II, Publ. Math. IHES. 2 (1980), [D3] P.Deligne. Cohomologie a supports propres, SGA4, LNM 30, [Dan] V.Danilov. Geometry of toric varieties, Russian Math. Surveys (Uspehy), t.xxxiii, 2(200), [DL] I.Dolgachev, V.Lunts. A character formula for the representation of the Weyl group in the eohomology of the associated toric variety, (to appear). [DV] M.Duflo, M.Vergne. Sur le foncteur de Zuckerman, C.R.A.S. Paris, t.304, Serie I, n, 1987, [Gi] J.Giraud. Cohomologie non abelienne, Springer-Verlag, [Go] R.Godement. Topologie algebrique et theorie des faisceaux, Hermann, Paris, 198. [GoMa] M.Goresky, R.MacPherson. Intersection Homology II, Invent. Math. 71, [Groth] A.Grothendieck. Sur quelques points d'algebre homologique, Tohoku Math. Journal, second series, vol.9, n 2, 3, 197. [H] R.Hartshorne. Residues and duality, LNM 20, [I1] L.Illusie. Complexe cotangent et deformations, LNM 239 (1971), 283 (1972). [KKMS-D] G.Kempf, F.Knudsen, D.Mumford, B.Saint-Donat. Toroidal embeddings, I, LNM a39 (1973). [Lu] D.Luna. Slices etales, Bull. Soc. Math. France, 1973, memoire 33. [S] E.Spanier. Algebraic topology, McGraw-Hill book company, [Sp] N.Spaltenstein. Resolutions of unbounded complexes, Compositio Mathematica 6: (1988). [Vel] J.-L.Verdier. Categories derivees, LNM 69, [Ve2] J.-L.Verdier. Dualite dans la cohomologie des espaces locmement compact, Sem. Bourbaki, 196/66, n 300.

2 Index A A~ Aa Aa,AM BG constructible space cartesian morphism cartesian functor Cx CX,G C Res( X ) Db(x) D+(X) D<-b(X),D>-~(X) mi(x) Df Dx D D+(XIY) D~(XIY) D~(X,,S) D (X) Dba(X,P) D~(X) D~(X) Dza( X, P) Db(~) Db /~ r m1(-filp) D,o(X) D+(X) D+(~) D+ (-fi]p ) D+(X,P) Db([G\X].) D~q([G\X].) DI,G Dx,a 104, , , 1 9 9, O

3 136 Db(Dx) 40 Db(Dx) 40 Db~h(DX) 40 D~(Dx) 40 DbG,h ( Dx ) 40 D~,~h ( mx ) 40 D~ 70 D~ 83 D + 83 D L<-b, D L>-a 91 D+(@S) 99 D( S) 99 decomposition theorem 42 de Rham complex 96 DG-algebra 68 DG-module 68 equivariant sheaf 2 equivariant eohomology (with compact supports) equivariant Poincare duality equivariant intersection 6 cohomology (with compact supports) f.,f!,f*,f! 6, 3 For 17 Fx 17 F 17 f0 17 f.h" 7 FI 63 Fs 63 free G-space fibered category 21 fiber C(~) of the fibered 21 category C --~ 7- fan G-space 2 G-map 2 [G\X]. G Res( X ) 4 good map 4 7x 100

4 137.~om Ha(X, F) Ha,c(X, F) oo-acyclic map oo-acyclic space oo-acyclic resolution oo-dimensional manifold ind(p) Ind. Ind! zca(x) zca(v, z.) IndVH lg IHa(X) IHa,c(X) invertible object integration functors ](:.4 /(:-projective /(:-flat G minimal ~-projective g(c) 6, 34, ~X s s s.)~.4 minimal complex m n-acyelic map n-acyclic space 10

5 138 n-acyclic resolution nice space C-map Perva(X) Perv(X) r r G+ = r q:x--~ X Q(p) q*: Db(X -) ~ nb(x ) Q~ = Q* Qf. = Q. R Res(X) = Re~(X, C) ReSH,G Res H RHom rkm rkam resolution compatible resolution trivial resolution induced resolution acyclic resolution multiplicative resolution Sha(X) Sh(X) S Sh/T Sh([C\X].) Sh~,([V\X].) S Res( X ) SK simplicial space ,

6 139 simplicial sheaf smooth base change smooth model of a classifying space T T<_b~ T>_a n t-category t-structure on D/~ triangulation of D~(X) toric variety X Xa 9, , 34 6, 2,

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