Unformatted text preview: a b -- F~b s (R f, (Qx/s (log D))) ( 1)b+'F~*b~(p~ Fa~ (~/T) | F*~ (R ~ + ~f, (~b/j (log D))) bs s ~ Fa*bs Rof, D)) (- '' . ... | g o +'/, (log D)) in which p is the cup-product with the Kodaira-Spencer class (1.1.3), viewed as a global section over S of 1 1 Os/r| R f, (Dero(X/S)). Before proceeding to the proof, we will recall some basic facts about the modular representation theory of finite groups of order prime to p, and then restate 3.2 "with a group of operators ". (3.2.1) Let G be a finite group of order prime to p, and k a field of characteristic p. Let V be a finite-dimensional k-space on which G acts as a group of k-automorphisms, through a homomorphism Z: G ~ GL(V). Denoting by F, bs: k~ k the absolute Frobenius endomorphism of k, the representation Z (v) of G on F.'~,s(V)=V| (where k is a module over k...
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- Fall '11
- finite group, Representation theory of finite groups, Modular representation theory, absolute Frobenius endomorphism, main technical result