Index A (module category), 3, 93 Ac,4 Ac-, 4, 93 A.7, 6 Aqc, 4 Aqct, 7 Aqczo 7 At, 7 Az, 7 A(U), 96 6• (Cech functor), 96 c=, 95, 97 cu, 97 D (derived category), 4, 93, 116 D:l::.,4 De, 94 De, 98 Dqc, 7, 54 r· (right adjoint of R/. o o o) jX, 5, 42, 117, 120 !',116 Jt, 8, 59 as homotopy colimit, 63 J'' 8, 42, 63, 76, 120 j#, 8, 64 JQ, 63 j, 5, 13, 36, 37,42, 98 jt, 57 r .. (torsion functor), 6, 94 Rr.. as homotopy colimit, 58 r.' .. , 6, 7 r := RT~ (cohomology colocalization), 24, 69 K (homotopy category), 4, 93 Kc-, 93 Ke, 94 :K~, 98 t~ c :K~. 98, 100 K(U), 96 Kr, 46 K:~ (limit of Koszul complexes), 49, 51, 108 Aij: Ui '-- Uj (i :J j E 'f!t), 96 L (left-derived functor), 4 A (homology localization), 8, 24, 54, 64, 69 AI (completion functor), 94 Ox (structure sheaf of ringed space X), 3 125 'f!t (subsets of {1, 2, o o 0, t} ), 96 Qx (quasi-coherator), 31, 35 Q!X. 48-49 q: K --- D (canonical functor), 93 qa, 94 q, 98 q: K(2lb)---. D(2lb), 100 R (right-derived functor), 4 RHom•, 42 p: De ...... De (equivalence)' 98 T (trace map), 5, 42, 120 TQ, 83 Tt, 18, 59 T#, 64 (}', 73 U (open cover), 96 U-module, 96 A(U) (U-module category), 96 K(U), 96 cu, 97 acyclic, 16 adic ring, 14 affine-I-acyclic, 100 affine-acyclic, 93, 100 base-change isomorphism, 8, 9, 77, 85, 89, 120 base-change map, 76 boundedness (way-outness) of .::l-functors, 5 Bousfield colocalization, 8, 69 Brown Representability, 5, 6, 59 coherence in categories, 115, 117, 119 continuous functor, 43 Deligne, Pierre, 5, 30, 43 .::l-adjoint, 4 .::l-functors (on triangulated categories), 4 composition of, 4 morphism between, 4 derived functor, 4 Duality Affine, 28 Coherent, see Grothendieck Duality Formal, 10, 22 http://dx.doi.org/10.1090/conm/244

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