Abstract
Let $G$ be a simple Chevalley group defined over $\mathbb{F}_{q}$. We show that if $r$ does not divide $q$ and $k$ is an algebraically closed field of characteristic $r$, then very few irreducible $kG$modules have nonzero $H^1(G,V)$. We also give an explicit upper bound for $\dim H^1(G,V)$ for $V$ an irreducible $kG$module that does not depend on $q$, but only on the rank of the group. Cline, Parshall and Scott showed that such a bound exists when $rq$. We obtain extremely strong bounds in the case that a Borel subgroup has no fixed points on $V$.

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PAGES = {416425},
ISSN = {00218693},
CODEN = {JALGA4},
MRCLASS = {20J06 (20G05 20G10)},
MRNUMBER = {1976701},
MRREVIEWER = {Christopher P. Bendel},
DOI = {10.1016/S00218693(02)006671},
ZBLNUMBER = {1019.20020},
}