By M. Raynaud (auth.), Michel Raynaud, Tetsuji Shioda (eds.)
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Additional resources for Algebraic Geometry: Proceedings of the Japan-France Conference held at Tokyo and Kyoto, October 5–14, 1982
2) induces . Therefore, HJ(zw~). are an d exact sequences. It was observed object W-modules : = ~im H J ( B W n ~ ) with coefficients cohomology) a) Operators sequence. = ~im HJ(HIWnn') and are related by exact and spectral somewhat spectral : HJ(HiW~')) (resp. boundaries, . 2). Note that in contrast (resp. H J ( B w ~ ) , plex. HJ(w~)'s : = ~im HJ(ZWn~i) HJ(HiWn'): (notations i > dim(X)-i an d the conjuqate In addition to the studied or (but not F , thus in general) nilpotent). is proper, of finite type HJ(ZWn~), HJ(BWn~), (cf.
By A complex R-grading and the HJ(M) of : thus will is is the u s u a l that every + n~O b_ndVn of W + n~ of W-modules, d whose satisfies FdV = d is an R-module and is the the ' as a left g r a d e d stated, the R components otherwise R-modules of . consider , where x bnFnd Unless M Dieudonn~ element O . ) deduced , and the c h a n g e M "j d , a V = Va ~ , ad = da b y abuse. R-module. M'" seen are e l e m e n t s R°-module in d e g r e e M(n) anFn R° and the d i f f e r e n t i a l R-modules M(n) i = M n+i a bicomplex biis R-module a left will be a left denote + n~O d ~ Mi+l R°-modules concentrated we'll as a finite a-nVn and ) Mi particular, it is e a s i l y written 0 and , Fa = a~F of (and maps b y the usual d to R-module (-l)nd of d e g r e e first d e g r e e R-module only graded which R-module n E ~ , we'll shift of degrees, o O) can be v i e w e d corresponds which .
The De Rham-Wit t complex. 2, the De Rham-Witt complex red as a sheaf of RF(X,W~') of R-modules D+(R) on d ) HJ(w~I) will be denoted RJF(w~" ) RF(X/W). 2. Coherent coherent For X proper, RF(X/W) for jth_ R-module ~RF(X,W~') is a perfect complex L = W~ is the (i) considered in the introduction. R-modules. e. ). The simple associated complex [15, II 2], and the spectral sequence F , can be conside- (with nonnegative first degree), whose cohomology row will be denoted HJ(wo) X . Applying W~ V R°-module), t o p o l o g i c a l l y nilpotent : finitely gene- ; such a module is an 31 extension V of an R°-module topologically nilpotent formal group) b y its over W k (k , F = V = : = by or H2(WO) which if X successive (in p a r t i c u l a r , is the b a s i c is the of m o d u l e s of the R-module F , d , V to quotients we w o n ' t use).
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.)