A Note on the Discontinuous Subgroups of the Orthogonal Group.
A note on the Hasse principle. Addenda
A spectral gap theorem in SU
We establish the spectral gap property for dense subgroups of SU, generated by finitely many elements with algebraic entries; this result was announced...
Addendum to: On volumes of arithmetic quotients of SO (1, n)
There are errors in the proof of uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.
An alternative proof of Scheiderer's theorem on the Hasse principle for principal homogeneous spaces.
Cayley orders
Charakterisierung von Drehungen und Bewegungen des Rn durch lineare Invarianten.
Classification of hermitian forms and semisimple gorups over fields of virtual cohomological dimension one.
Cyclotomic equations and square properties in rings.
Definite Lattices Over Real Algebraic Function Domains.
Deformation Retracts with Lowest Possible Dimension of Arithmetic Quotients of Self-Adjoint Homogeneous Cones.
Die unimodularen Substitutionen in einem algebraischen Zahlenkörper
Embeddings of maximal tori in orthogonal groups
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic to contain a maximal torus of a given type.
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
Erzeugung ganzzahliger orthogonaler Gruppen durch Spiegelungen.
Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low dimensions, both polynomial isoperimetric inequalities and finiteness properties. As a tool in our proof, we establish polynomial isoperimetric inequalities and finiteness properties for certain solvable groups that appear as subgroups of parabolic groups in semisimple groups, thus generalizing a theorem of Bux....
Finite subgroups of .
Finiteness properties of soluble arithmetic groups over global function fields.
Free Quotients of Congruence Subgroups of SL2 Over a Coordinate Ring.
Galois cohomology of the classical gorups over fields of cohomological dimension ... 2.