On arithmetic in Mordell–Weil groups

on finite arithmetic groups

let $f$ be a finite extension of $bbb q$‎, ‎${bbb q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $e/f$ be a galois extension‎. ‎we study the realization fields of‎ ‎finite subgroups $g$ of $gl_n(e)$ stable under the natural‎ ‎operation of the galois group of $e/f$‎. ‎though for sufficiently large $n$ and a fixed‎ algebraic number field $f$ every its finite extension $e$ is‎ ‎re...

Arithmetic groups

The theory of arithmetic groups deals with groups of matrices whose entries are integers, or more generally, S-integers in a global field. This notion has a long history, going back to the work of Gauss on integral quadratic forms. The modern theory of arithmetic groups retains its close connection to number theory (for example, through the theory of automorphic forms) but also relies on a vari...

Arithmetic Groups

We present detailed summaries of the talks that were given during a weeklong workshop on Arithmetic Groups at the Banff International Research Station in April 2013, organized by Kai-Uwe Bux (University of Bielefeld), Dave Witte Morris (University of Lethbridge), Gopal Prasad (University of Michigan), and Andrei Rapinchuk (University of Virginia). The vast majority of these reports are based on...

Algebraic Groups and Arithmetic Groups

Arithmetic Groups Acting on Compact Manifolds

In this note we announce results concerning the volume preserving actions of arithmetic subgroups of higher rank semisimple groups on compact manifolds. Our results can be considered as the first rigidity results for homomorphisms of these groups into diffeomorphism groups and show a sharp contrast between the behavior of actions of these groups and actions of free groups. Let G be a connected ...