By M. Raynaud (auth.), Michel Raynaud, Tetsuji Shioda (eds.)

ISBN-10: 3540126856

ISBN-13: 9783540126850

ISBN-10: 3540386769

ISBN-13: 9783540386766

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Extra resources for Algebraic Geometry: Proceedings of the Japan-France Conference held at Tokyo and Kyoto, October 5–14, 1982

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In R-module R-modules, an is the are as to the jth-row of M'', 30 (... of ~ HJ(M) i M'" ) HJ(M) i+l . ) n 6 ~ , the shift c o r r e s p o n d i n g to the first second) degree will be denoted by D(R) jth -cohomology which is the (n) (resp. row (resp. In]). We'll denote by the derived category of the (abelian) category of (graded) R-modules (and maps of degree O). 2) > H~(sM) defined by the filtration of ~M , by the first degree. g. if is uniformly bounded. to The functor D(W). One defines in an obvious way the notion of sheaf of (graded) R-modules on the k-scheme D(X,R).

Because it is so difficult to calculate the E1 term of (I), it was desirable to produce a manageable criterion for the finiteness of the criterion, Ekedahl, HJ(w~)'s . Under some mild restrictions, such a involving only Newton and Hodge polygons, has b e e n given by in answer to a question of Katz. His method uses in a curious way the formalism of t-structures of Deligne [2]. A concept that has g r a d u a l l y emerged as the main technical tool in the four questions above is the notion of graded module over a certain graded ring R O = W~[F,V].

7) ~ . One can also recover Poincar~ duality at L R n ® R - . 6) Berthelot's Hom (D being but it takes much longer this way. 4. Applications. 2). 2), )- R i + J F ( w n ") . 10). In order to explain what happens, lowing notations and terminology. 2) AiM A~il M~ (in particular, with A ss 1 : = TiM/Ti+IM , A~sM : = TiM/p-tors : = p-tors(M)/T2M , , A~il M : = Heart (T2M) we have a canonical decomposition of semi-simple torsion and A nil 1 A1 = A1 @ A1 ss nil ' of positive slope). 3) d o m ij in d e g r e e (i,j), a n d w e ' l l a l s o d e n o t e (cf.

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Algebraic Geometry: Proceedings of the Japan-France Conference held at Tokyo and Kyoto, October 5–14, 1982 by M. Raynaud (auth.), Michel Raynaud, Tetsuji Shioda (eds.)

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