Index * (concatenation of labeled sequences), 208 == (labeled sequence), 208 -~ (Coz0-valued pseudofunctor on lFc), 7 _b (Cousin-complex functor associated to a closed immersion), 72 -~ (covariant pseudofunctor on It), 52, 144 (-)x, 200 (-)0 , 200 (-)', 202 (-)b, 204 (-) 181 , 208 { }~ (Ac(Spf(A))-sheaf associated to the A-module {} ), 15 A{s-1} (completed localization), 18 A{!} (S={f,j2,J3 , ... }), 18 A (abelian category), 11 A( X) (category of Ox-complexes on ringed space (X,Ox)), 11 A?(X) (full subcategory of A(X)), 11 Ac(X) (coherent subcat. of A(X)), 11 Ac(X) (1!!!1-coherent subcat. of A( X)), 11 Aqc(X) (quasi-coherent subcat. of A(X)), 11 At(X) (torsion subcat. of A(X) on formal scheme X), 19 Act(X) (:= Ac(X) n At(X)), 19 Aqct(X) (:= Aqc(X) n At(X)), 19 (3. (base-change isomorphism), 200 B~, 204 B~, 205 B~, 257 Bs, 256 !3., 209 f3s, 212 is well defined, 214 f3ul '"2' 226 Cou(X) (Cousin complex category on X), 42 CozLl. (Cousin Aqct complexes category), 5, 40 Coz~ (CozLl.-complexes with 0 differen- tial), 5 C(A) (category of A-complexes), 11 C(X) := C(A(X)), 11 273 C F1 ,F2 , 208, 218 C, 200 e (pseudofunctorial cover)' 202 c'f!_ ),(-) (comparison isomorphism for generic pseudofunctor -#), 45, 199 It (complete local rings subcategory), 4 CM(X, .::l) (subcategory of D ict(X)), 143, 178 CM* (X, .::l), 143, 191 8-functor, 12 8'f!-) (unit isomorphism for generic pseudo- functor -#), 45, 263 d (universal derivation) for continuous homomorphisms, 23 for formal-scheme maps, 27 dsep (universal separated derivation), 23 d( (differential of a complex c•), 11 D(A) (derived category of A-complexes), 11 D(X) := D(A(X)), 11 D7(X) c D(X) (homology in A?(X)), 11 Dt (X) c D?(X) (homologically bounded below), 11 D? (X) C D7(X) (homologically bounded above), 11 D~(X) (essential image of Dc(X)), 108, 142, 187 fi (X)(=RT{- 1 (D~(X)nD+(X))), 143, 187 Dqc(X) (= Rr{- 1 (Dqc(X))), 142 o+(X .::l)cM (.::l-CM complexes subcat. of o+(X)), 41 Dx, 200 Vn (dualizing functor), 187 'Dt (torsion-dualizing functor), 108 Ll, see codimension function .::l-CM (Cohen-Macaulay w.r.t. codimen- sion function .::l), 41 .::l-Cousin complex, 40 Derc (continuous derivations), 23 €, 203 E_M., 114
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