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Isocrystals with additional structure. II

Published online by Cambridge University Press:  04 December 2007

ROBERT E. KOTTWITZ
ROBERT E. KOTTWITZ
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Avenue, IL-60637-1546, Chicago, U.S.A.; e-mail: kottwitz@math.uchicago.edu
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Abstract

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Let $F$ be a $p$-adic field, let $L$ be the completion of a maximal unramified extension of $F$, and let $\sigma$ be the Frobenius automorphism of $L$ over $F$. For any connected reductive group $G$ over $F$ one denotes by $B(G)$ the set of $\sigma$-conjugacy classes in $G(L)$ (elements $x,y$ in $G(L)$ are said to be $\sigma$-conjugate if there exists $g$ in $G(L)$ such that $g^-1 \kappa \sigma(g)=y$. One of the main results of this paper is a concrete description of the set $B(G)$ (previously this was known only in the quasi-split case).

Keywords

Isocrystals$p$-adic fieldslinear algebraic groups
Type
Research Article
Information
Compositio Mathematica , Volume 109 , Issue 3 , December 1997 , pp. 255 - 339
Copyright
© 1997 Kluwer Academic Publishers