Dr. Katz DEq Homework Solutions 18

Dr. Katz DEq Homework Solutions 18 - whose precise...

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18 N.M. Katz: (2.1.1.1) which satisfies (2.1.1.2) (2.1.1.3) (2.1.1.4) (2.1.2) cg-1 : f2jc,~,/s (log Dtp)) ~, ~t ~i (F, (Q~/s (log O))) .-1(1)=1, (~-- 1(0) A ~') = (~- a (0)) A ~- 1 (T), c~-, (d(a- 1 (x))) = the class of x p- 1 dx. Putting together all the conditions, we see that, in terms of the local coordinates xl, . .., x. chosen in (1.0.3.1), we have cg- 1 (h) = the class of F- 1 (h) for h a local sections of Cx~p~ ~e_ 1 ( d~-l(xv)] dx~ (2.1.2.1) a-X(xv) ] =the class of x~ , for v = 1, . .., a \ c~-l{da-l(xi))=the class ofx~-'dxj for j=~+l . ... , n. 2.2. General Nonsense We must now give a tautology on functorial spectral sequences,
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Unformatted text preview: whose precise formulation is somewhat lengthy. (2.2.1) Suppose given f: Y-~ Z an arbitrary morphism of schemes. For every Z-scheme ZI, we form the fibre product Yz,= Yxz Z~, which sits in the cartesian diagram Yzl ~ Y Z, - --~ Z. Suppose we are give, for every Z-scheme Za, a finitely filtered complex (non-zero only in positive degrees). (Kz,, F) of fz~l((.Oz,) modules on Yz,, which is functorial in the variable Z-scheme Z1 in the following sense: (2.2.1.2) For any morphism ~0:Z2~Z1 of Z-schemes, denote by ~0r: Yz, ~ Yz, the induced morphism, which sits in the commutative diagram (2.2.1.3) Y - Z2 e , Za Y...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.

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