First cohomology groups of Chevalley groups in cross characteristic

Robert M. Guralnick, Pham Huu Tiep

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

Let G be a simple Chevalley group defined over Fq. 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 H1(G, V). We also give an explicit upper bound for dim H1(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 r|q. We obtain extremely strong bounds in the case that a Borel subgroup has no fixed points on V.

Original languageEnglish (US)
Pages (from-to)543-559
Number of pages17
JournalAnnals of Mathematics
Volume174
Issue number1
DOIs
StatePublished - Jul 1 2011

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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