Vladimir Chernousov - Academia.edu (original) (raw)

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Papers by Vladimir Chernousov

Pacific Journal of Mathematics, 2015

The Michigan Mathematical Journal, Oct 1, 2008

If Gamma is a nonuniform, irreducible lattice in a semisimple Lie group whose real rank is greate... more If Gamma is a nonuniform, irreducible lattice in a semisimple Lie group whose real rank is greater than 1, we show Gamma contains a subgroup that is isomorphic to a nonuniform, irreducible lattice in either SL(3,R), SL(3,C), or a direct product SL(2,R)^m x SL(2,C)^n$, with m + n > 1. (In geometric terms, this can be interpreted as a statement about the existence of totally geodesic subspaces of finite-volume, noncompact, locally symmetric spaces of higher rank.) Another formulation of the result states that if G is any isotropic, almost simple algebraic group over Q (the rational numbers), such that the real rank of G is greater than 1, then G contains an isotropic, almost simple Q-subgroup H, such that H is quasisplit, and the real rank of H is greater than 1.

Comptes Rendus Mathematique, Sep 15, 2007

Let k be a field of characteristic zero, and let G be a split simple algebraic group of type G2 o... more Let k be a field of characteristic zero, and let G be a split simple algebraic group of type G2 over k. We prove that the functor R↦He´t1(R,G) of G-torsors satisfies purity for regular local rings containing k. To cite this article: V. Chernousov, I. Panin, C. R. Acad. Sci. Paris, Ser. I 345 (2007).