Dr. Katz DEq Homework Solutions 105

Dr. Katz DEq Homework Solutions 105 - Algebraic Solutions...

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Algebraic Solutions of Differential Equations 105 integrable T-connection V,~ on (gs is a p-linear mapping (7.1.0) 0,~: Der(S/T) ~ Endr (9 s which is additive in the variable closed one-form o9. (7.1.1) Recall from (6.0.2.5) the commutative diagram (in which g: S --~ T is the structural morphism) S., F ~ S (p) ~ ~, S v ) S(p) T Fabs ~T the middle square of which is cartesian. (7.1.2) Proposition. The p-curvature 0o, of Vo is given by the formula (7.1.2.0) 0o (D) = F* ((a* (o9)- cg(o9), r (D))) where ~ is Cartier's isomorphism (2.2.1) jr (F, f2~/r) ~ ' ~s'(,,/r (applied to the class of the closed form o9), ~* (D) is the T-derivation of S (p) defined by (7.1.2.1) a*(D)(a*(f))=a*(D(f)), f a local section of (gs, and (,) is the canonical pairing of Os~prmodules
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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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