Unformatted text preview: braic extension L/K such that (N, V)| L has p-curvature zero for almost all peZ. K Putting together (5.4.1) and (126.96.36.199), we have the obvious (5.4.4) Proposition. Let (N, 17) be a differential equation over a function field K/C (188.8.131.52). If (N, 17) has a full set of algebraic solutions, then it has p-curvature zero for almost all primes p. (5.4.5) Let K/C be a function field, and let Ux be a smooth quasi-projec- tive K-variety. By Hironaka (), we can find a projective and smooth K-variety 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 S-scheme f: X--* S and divisors D~ in X which are smooth...
View Full Document
- Fall '11
- Prime number, function field, integrable connection, smooth divisors D~