"Super-rigid non- arithmetic group; A counter example to Platonov conjecture."
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My title will be: Super-rigid non- arithmetic group; A counter example
to Platonov conjecture.
Abstract: The celebrated theorem pf Margulis says that lattices
(=discrete subgroups of finite covolume) in higher rank Lie groups are
super-rigid and arithmetic. Platonov conjectured that any linear
super-rigid group is of arithmetic type. The conjecture could have nice
applications. We present counter examples which shows that our
understanding of linear groups is still far from being satisfying. The
idea of the construction is based on ideas applied to answer
Grothendieck's problem on maps between pro-finite completions.
(joint work with Hyman Bass).