Algebraic Geometry: Proceedings of the Japan-France by M. Raynaud (auth.), Michel Raynaud, Tetsuji Shioda (eds.)

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

Example text

Recently, simpler definition : the key o b s e r v a t i o n Going tral over the further, sequence structure (Cohen-Macaulay) Thanks W~ we h a v e (2) which unfortunately of the constructions slope of by considering complex scheme a natural rather D(W). than viewed He states in t u r n m a k e s (even the i n f i n i t e be p e r f e c t Ekedahl a new, (where perhaps the De R h a m W i t t , considered as a c o h e r e n t m a p and the m u l t i p l i c a t i v e as an objet a general ) W , in general, of a).

5 to RF(X,W~'). 2) given by sequence) E~ j = H J ( w ~ ) and obtain that W-modules. 3) G~ j) HJ(wc~)/V-torsion G 13 , whose is p-divisible up to isogeny corresponds (rasp. H J ( w ~ ) / V - ~ Z + V ) , M = RF(X,WQ'). HJ(w~), is defined by the open subgroups (rasp. 2) degenerates v n H J ( w ~ i) + d V n H 3 ( W ~ - I ) . part of the is finite dimen- being proper. 7, is assumed to be proper. 2 hl3's invariant. Connections between the will be discussed (ii), that we have : Tl3's in §6. 4) (HJ(w~) The following is finitely generated vanishing property over W) < > (T ij = T i-l'j = 0).

The : D(R) in M^ L : = R ~ i m R. ) M in R-module, induced R. ® R M D(R), . 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..

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