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- W2273284294 abstract "Let $G$ be the simple algebraic group $mathrm{SL}_2$ defined over an algebraically closed field $k$ of characteristic $p > 0$. Using results of A. Parker, we develop a method which gives, for any $q in mathbb{N}$, a closed form description of all simple modules $M$ such that $mathrm{H}^q(G,M) neq 0$, together with the associated dimensions $mathrm{dim}mathrm{H}^q(G,M)$. We apply this method for arbitrary primes $p$ and for $q leq 3$, confirming results of Cline and Stewart along the way. Furthermore, we show that under the hypothesis $p > q$, the dimension of the cohomology $mathrm{H}^q(G,M)$ is at most 1, for any simple module $M$. Based on this evidence we discuss a conjecture for general semisimple algebraic groups." @default.
- W2273284294 created "2016-06-24" @default.
- W2273284294 creator A5022205517 @default.
- W2273284294 date "2014-11-05" @default.
- W2273284294 modified "2023-09-27" @default.
- W2273284294 title "On The Cohomology of $mathrm{SL}_2$ with Coefficients in a Simple Module" @default.
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