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math.GR2022
Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings
Peter Abramenko, Andrei S. Rapinchuk, Igor A. Rapinchuk
We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive…
math.GR2022
Algebraic groups with good reduction and the genus problem
Igor A. Rapinchuk
We first provide an overview of several results dealing with the genus of a division algebra and highlight the role of ramification in its analysis. We then give a survey of recent…