Vol. 7, No. 5, 2013

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Weakly commensurable $S$-arithmetic subgroups in almost simple algebraic groups of types $\mathsf{B}$ and $\mathsf{C}$

Skip Garibaldi and Andrei Rapinchuk

Vol. 7 (2013), No. 5, 1147–1178
Abstract

Let G1 and G2 be absolutely almost simple algebraic groups of types B and C, respectively, defined over a number field K. We determine when G1 and G2 have the same isomorphism or isogeny classes of maximal K-tori. This leads to the necessary and sufficient conditions for two Zariski-dense S-arithmetic subgroups of G1 and G2 to be weakly commensurable.

Keywords
isogenous maximal tori, weak commensurability, isomorphic maximal tori
Mathematical Subject Classification 2010
Primary: 20G15
Secondary: 11E57, 14L35, 20G30
Milestones
Received: 20 January 2012
Revised: 29 April 2012
Accepted: 7 June 2012
Published: 6 September 2013
Authors
Skip Garibaldi
Institute for Pure and Applied Mathematics
460 Portola Plaza
Box 957121
Los Angeles, CA 90095-7121
United States
http://www.mathcs.emory.edu/~skip/
Andrei Rapinchuk
Department of Mathematics
University of Virginia
Charlottesville, VA 22904
United States
http://www.math.virginia.edu/Faculty/Rapinchuk/