TY - JOUR
T1 - First cohomology groups of Chevalley groups in cross characteristic
AU - Guralnick, Robert M.
AU - Tiep, Pham Huu
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2011/7
Y1 - 2011/7
N2 - 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.
AB - 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.
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U2 - 10.4007/annals.2011.174.1.16
DO - 10.4007/annals.2011.174.1.16
M3 - Article
AN - SCOPUS:79959986453
VL - 174
SP - 543
EP - 559
JO - Annals of Mathematics
JF - Annals of Mathematics
SN - 0003-486X
IS - 1
ER -