By M. Raynaud (auth.), Michel Raynaud, Tetsuji Shioda (eds.)
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Extra resources for Algebraic Geometry: Proceedings of the Japan-France Conference held at Tokyo and Kyoto, October 5–14, 1982
On given Hn(x/w) compatible with ~ a) are s a t i s f i e d . 4 It was p r o p o s e d the c o n d i t i o n s b) of is H o d g e - W i t t in each d e g r e e varieties X consists is c a l l e d in [161 HJ(Bw~) = 0 as close as p o s s i b l e for all for example, group is of of K3 n height. [20~. this o_~n Hn(x/W), Hn-i(zw~) decompositions X Hodqe-Witt analogous varieties = 0 to sense if it of K a t o  to Hodge-Witt varieties are varieties (in aspects : i , j , and it is shown in a d i f f e r e n t with if the supersingular Hodge-Witt in c o n n e c t i o n n of H o d g e - W i t t is e q u i v a l e n t sense, while class in the for all seem to live Polygonal in d e g r e e decomposition is said to be H o d q e - W i t t condition where ~ is H o d q e - W i t t i , j .
7 they i m p l y PROPOSITION D(R) is an i s o m o r p h i s m if M L W n ® W - ' n } 1 . In p a r t i c u l a r , and N are in Db(R) (cf. 10). 3. D u a l i t Y . 3)). zing functor. 5) DM~DN D~(R) o n t o itself. : = RHOmW(-,W). 8) and --~-~ D ( M % N) . 6) where p as it m a y because R~ the of the the functor alternate D is not so h a r d description. 7) : D(R) On the o t h e r hand, between R • D(R) interchanging and the o p p o s i t e a functor from fractions of D(R) ° p p W). 3). i >2 . 10) M slope zero positive D°M DIM D2M HOmw(M,W) 0 0 0 HOmw(M,W)(1) 0 O HOmw(M,K/W) O slope semi-simple nilpotent torsion torsion u =l In this table, zero R-module slope, with finite a finitely M semi-simple F bijective, length with 0 O HOmw(M,K/W)(1) 0 0 u- - l( 2 ) = generated is r e s p e c t i v e l y torsion, nilpotent torsionfree F over called bijective, with W , concentrated of slope torsion F if zero, M is t o r s i o n f r e e topologically of finite length in d e g r e e positive with nilpotent, F of nilpotent.
Various smooth for- In p a r t i c u l a r , = dimk(Mi/V-~Zi)/v . On the o t h e r hand, t h e r e are i n c l u s i o n s F~B 1 c V - t o r s ( M l) c V-~Z 1 , with V-tors(Mi)/F~B i b3) Finally, M , denoted one can c o n s i d e r F-tors(M), In c o n t r a s t w i t h general, of finite l e n g t h o v e r and closure in M of the s u b - W - m o d u l e of F-tors(M) (this h a p p e n s M (defined b y F-tors(M). V-tots(M), F F~B i = 0). Nor is it c l o s e d in M . F-torsion w h i c h is in e a c h d e g r e e a s u b - R ° - m o d u l e p-tots(M) k i l l e d b y a p o w e r of nite t o p o l o g y of W is not, in d e g r e e i of of M .
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