Nonarchimedean superrigidity of solvable S-arithmetic groups

JOURNAL OF ALGEBRA

卷:416

Article

Morris, Dave Witte¹  Studenmund, Daniel² 

[1] Univ Lethbridge, Dept Math & Comp Sci, Lethbridge, AB T1K 3M4, Canada

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

关键词: Superrigidity;    Solvable group;    Algebraic group;    S-arithmetic group;    Representation;   

DOI  :  10.1016/j.jalgebra.2014.06.018

来源: Elsevier

【 摘 要 】

Let Gamma be an S-arithmetic subgroup of a solvable algebraic group G over an algebraic number field F, such that the finite set S contains at least one place that is nonarchimedean. We construct a certain group H = <((Res(F/Q) Gamma))over bar>(char) (Gamma)(S) , such that if L is any local field and alpha: Gamma -> GL(n)(L) is any homomorphism, then a virtually extends (modulo a bounded error) to a continuous homomorphism defined on some finite-index subgroup of H. In the special case where F = Q, rank(R) G = 0, and Gamma is Zariski-dense in G, we may let H = G(S). We also point out a generalization that does not require G to be solvable. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free