Dr. Katz DEq Homework Solutions 75

Dr. Katz DEq Homework Solutions 75 - Algebraic Solutions of...

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Algebraic Solutions of Differential Equations 75 (5.1.1) Then after the change of base Spec(C)--* T, Dc .-* D X c ~ X (5.1.1.0) 1 Sc-----~S Spec(C) --, T the coherent sheaf with integrable connection on S c (5.1.I.1) (R"fc,(~ic/sc(log D)), V becomes trivial on a finite ~tale covering q~ : S' --* S c, i. e., becomes isomorphic to (((gs,) ~ d), where b,=the rank of R"f,(f~/s(logD) ) over the generic point of S. Proof. By (4.3.3), it suffices to prove that the Hodge filtration F on R"fc,(~}c/sc(log Dc)) is horizontal for the Gauss-Manin connection. For this it suffices to prove that the Hodge filtration is horizontal over ~c, since the obstruction to the horizontality is the (gsclinear Kodaira-
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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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