12 citations · 38 across the 17 of their papers we have counts for
22 papers
Loop torsors. Theory and applications
Philippe Gille, Vladimir Chernousov, Arturo Pianzola
Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theo…
A characterization of groups of type arising from the first Tits construction
Vladimir Chernousov, Alexandre Lourdeaux, Arturo Pianzola
We show that algebraic groups of type (or equivalently Albert algebras) arising from the first Tits construction are determined uniquely by their invariant.
Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
We provide a new condition for an absolutely almost simple algebraic group to have good reduction with respect to a discrete valuation of the base field which is formulated in term…
-triviality of Groups of Type Arising from the First Tits Construction
Seidon Alsaody, Vladimir Chernousov, Arturo Pianzola
Any group of type is obtained as the automorphism group of an Albert algebra. We prove that such a group is -trivial whenever the Albert algebra is obtained from the…
On the Tits-Weiss Conjecture and the Kneser-Tits Conjecture for and
Seidon Alsaody, Vladimir Chernousov, Arturo Pianzola
We prove that the structure group of any Albert algebra over an arbitrary field is -trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conje…
The finiteness of the genus of a finite-dimensional division algebra, and some generalizations
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applic…