Unformatted text preview: kKP is an isomorphism. Thus it remains to prove only that (6.0.2.9) is an isomorphism if and only if its source and target have the same dimension. This is indeed the case, because (6.0.2.9) is always injective; in fact we have the apparently more general (6.0.3) Proposition. Let T be a scheme of characteristic p, S a smooth Tscheme, and (M, V) a quasicoherent (gsmodule with integrable T connection. The canonical mapping ( cf the diagram (6.0.2.7)) (6.0.3.0) F, (M v)  (gs = F* (F, (MY)) ~ M is always injective. Proof The question is local on S, so we may assume S is 6tale over A~ via X1, . .., X,. Then (9 s is a free FX(~s~,~)module with basis the monomials X wd~f'n xW'. .. X w" having 0< Wi <p 1. Thus we must show 6 Inventiones math., Vol. 18...
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 Fall '11
 NormanKatz
 Trigraph, Rational number, Algebraic Solutionsof DifferentialEquations

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