Abstract

Let G be a connected, simply connected, quasisimple algebraic group over an algebraically closed field of characteristic p > 0, and let V be a rational G-module such that dimV ≤ p. According to a result of Jantzen, V is completely reducible, and H¹(G,V ) = 0. In this paper we show that H²(G,V ) = 0 unless some composition factor of V is a nontrivial Frobenius twist of the adjoint representation of G.

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