By M. Raynaud (auth.), Michel Raynaud, Tetsuji Shioda (eds.)
ISBN-10: 3540126856
ISBN-13: 9783540126850
ISBN-10: 3540386769
ISBN-13: 9783540386766
Read or Download Algebraic Geometry: Proceedings of the Japan-France Conference held at Tokyo and Kyoto, October 5–14, 1982 PDF
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Additional info for Algebraic Geometry: Proceedings of the Japan-France Conference held at Tokyo and Kyoto, October 5–14, 1982
Example text
1. a) The and Fix an i n t e q e r following conditions are e q u i v a l e n t is f i n i t e l y qenerated over W for i+j = n ; - H J ( H i W ~ ") is f i n i t e l y generated over W for i+j = n ; - HJ(zw~) is f i n i t e l y qenerated over W for i+j = n o__rr n+l - HJ(Bw~) is f i n i t e l y generated over W for i+j = n o__rr n+l b) A s s u m e the c o n d i t i o n s P. 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.
_ ....... 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 .
Set . 4) for all in b) n D-(R), If X/k complete on WnX . W e say M M ^ (which is a g a i n : this DEFINITION is c o m p l e t e is of finite follows . 6. 4) ~ M ^ . 7 : a) For as implies of M shows. 2) for all i . W_~e 34 denote by D~(R) the full subcateqory of D(R) consistinq of coherent complexes. 7. Let lent M E Db(R). 8. Db(R) is a trianqulated C if two vertices of a (distinquished) i_~s, too). e. the third o_~f Mod(R) con- is an abelian subcateqory closed under extensions.. 9 (cf. 8]). Let tions are equivalent (i) M (ii) M over W n (iii) M The followinq condi- : is coherent ~ , ~im M n for all M E Mod(R).
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.)
by Daniel
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