On the congruence subgroup problem, II.
On the Congruence Subgroups Problem: Determination of the "Metaplectic Kernel".
On the congruence-subgroup problem for some anisotropic algebraic groups over number fields.
On the Group of Norm 1 Elements in a Division Algebra.
On the homology of the special linear group ove a number field.
On the Homomorphisms of the Integral Linear Groups.
On the isomorphisms of the projective orthogonal groups and their congruence subgroups.
On the macimality of ... in ...
On the Projective Class Group of Arithmetic Groups.
On the structure of algebraic groups over global fields.
On varieties of Hilbert type
A variety over a field is of Hilbert type if is not thin. We prove that if is a dominant morphism of -varieties and both and all fibers , , are of Hilbert type, then so is . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.
On volumes of arithmetic quotients of
We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of . As a result we prove that for any even dimension there exists a unique compact arithmetic hyperbolic -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We...
Principe de hasse faible pour les systèmes de formes quadratiques.
Projective simplicity of groups of rational points of simply connected algebraic groups defined over number fields
Quasiflats with holes in reductive groups.
Quelques questions d’approximation faible pour les tores algébriques
Soient un corps global, un -tore, un ensemble fini de places de . On note le complété de en . Soit , resp. , le groupe des points -rationnels, resp. -rationnels, de . Notons le sous-groupe compact maximal. Nous montrons que pour et convenables l’application induite par l’application diagonale n’est pas surjective. Cela implique que pour convenable le groupe ne couvre pas forcément toutes les classes de -équivalence de . Lorsque est un corps de fonctions d’une variable...
Radix redux: Normal subgroups of symplectic groups.
Rational fixed points for linear group actions
We prove a version of the Hilbert Irreducibility Theorem for linear algebraic groups. Given a connected linear algebraic group , an affine variety and a finite map , all defined over a finitely generated field of characteristic zero, Theorem 1.6 provides the natural necessary and sufficient condition under which the set contains a Zariski dense sub-semigroup ; namely, there must exist an unramified covering and a map such that . In the case , is the additive group, we reobtain the...
Rational Homology of Bianchi Groups.
Real Strict Localizations.