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Unformatted text preview: finite rank, and to degenerate at E~. (5.1) Theorem. Hypotheses as in (5.0.0), let n>O be an integer. Suppose that there is some non-void affine open set ~ c S satisfying (5.0.1), and an infinite set $ of prime numbers p, such that the following condition (5.1.0) holds (5.1.0) For every point of Twith values in (the spectrum of) a finite field Fq of characteristic peS,, after the base change Spec(Fq)---~ T, (5.1.o.o) D~ | , D~, 1 l 1 ~| , ~- 1 1 Spec(Fq) , T ~D [ ,X .,S the p-curvature of the free (Qall(~AFq module with integrable connection relative to Fq (5A.o.1) (R"f, ((2~-/s (log D))tq/, V)@Fq is zero, in other words, that the inverse image of R"f,(f2"x/s(logD)) on | Fq is spanned by its horizontal sections....
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- Fall '11