Unformatted text preview: braic extension L/K such that (N, V) L has pcurvature zero for almost all peZ. K Putting together (5.4.1) and (5.4.3.3), we have the obvious (5.4.4) Proposition. Let (N, 17) be a differential equation over a function field K/C (5.4.3.2). If (N, 17) has a full set of algebraic solutions, then it has pcurvature zero for almost all primes p. (5.4.5) Let K/C be a function field, and let Ux be a smooth quasiprojec tive Kvariety. By Hironaka ([18]), we can find a projective and smooth Kvariety Xx which contains UK as an open set, such that the complement DK = XK UK is a union of smooth divisors D~, ~ in XK which have normal crossings. By "general nonsense", we can find a finitely generated sub ring A of C, a smooth Spec(A)scheme S with geometrically connected fibres such that K is the function field of its complex fibre So, a projective and smooth Sscheme f: X* S and divisors D~ in X which are smooth...
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 Fall '11
 NormanKatz
 Prime number, function field, integrable connection, smooth divisors D~

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