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

Example text

5) is not, in general, (hence finitely generated over even if W). 7]. 4) and H~(X/W) H ~ ( W ~ ~) of H ~ (W~), but rather mod F n . e. 4. 2. M u l t i p l i c a t i o n in ~" W n defines a map of D(Wn[d])~. 3) can in fact be viewed as a map of RF(Wnn') , D(Wn[d]) ) Wn(-N)[-N] : . e. defines an isomorphism of RF(Wn~') D(Wn[d]) ~ D(RF(Wnn'))(-N)[-N] D = RHom(-,Wn). 1. 3. Ekedahl's duality theorem. We assume from now on dga-structure X is proper. 4). 4) pNF W . }. D(RF(Wn'))(-N)[-N] (Ekedahl). 4) is an isomorphism.

T r a c e m a p ( W n f ) ! 2) , is the p r o j e c t i o n . Wn+I~[N] adjunction). Thus (resp. 4) (resp. 1). c o m p l e x on c o m p l e x is c o n c e n t r a t e d as is well k n o w n followinq one has a c Q m m u t a t i v e tr [ w h e r e the u p p e r These isomorphisms ~ i~Wn~[N] (Wn+if)'Wn+ 1 dualizing i s o m o r p h i s m of : Wn f : WnX i : Wn x r is a n a t u r a l WnX .

2) the ring given by right of RI/(vnR 1 +dVnR°)) d). 2) to R), and the l i f t i n g of d : R n ~ Rn(1) 0 1 (0 0 ) in d e g r e e -i . One can -2 , and D(R). 5) L R1 ® R W~" ~ , Wn~" and in p a r t i c u l a r , for n=l , ~ , ~" , w h i c h is the key link b e t w e e n De R h a m - W i t t and De Rham. 6) for D(W L Wn ® W ~ M M in n induces ~ Rn ) : L ~ > ~ ( R n ® R M) D+(R). 7. 8) where x sending R E(x)' homogeneous formal a n a l o g y b e t w e e n a Cartier isomorphism r e a s o n for this is that if to n ~ 1 .

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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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