Infinite Symplectic Groups over Rings
Intermediate subgroups of the Steinberg groups over the field of fractions of a principal ideal ring.
Isomorphic Chevalley groups over integral domains
-theory and stable algebra
Lattices in product of trees
Le groupe fondamental des groupes linéaires
Le théorème d'Eichler sur le nombre de classes d'idéaux d'un corps de quaternions totalement défini et la mesure de Tamagawa
Local-global principle for congruence subgroups of Chevalley groups
Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and...
Manin’s and Peyre’s conjectures on rational points and adelic mixing
Let be the wonderful compactification of a connected adjoint semisimple group defined over a number field . We prove Manin’s conjecture on the asymptotic (as ) of the number of -rational points of of height less than , and give an explicit construction of a measure on , generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points on . Our approach is based on the mixing property of which we obtain with a rate of convergence.
Metaplectic covers of and the Gauss-Schering lemma
The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a -cocycle corresponding to a higher metaplectic extension of GL for any global field . In the case that has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity...
Normal subgroups of classical groups over Banach algebras.
On algebraic tori of norm type.
On certain closed subgroups of .
On mutual commutants of generalized carpet subgroups.
On normal subgroups of over rings with many units
On overgroups of and in their minimal representations.
On subgroups of GL2 over non-commutative local rings which are normalized by elementary matrices.
On symplectic groups over polynomial rings.
On the congruence subgroup problem, II.
On the Congruence Subgroups Problem: Determination of the "Metaplectic Kernel".