5 papers · 1 filter
Recent developments in the theory of linear algebraic groups: Good reduction and finiteness properties
Andrei S. Rapinchuk, Igor A. Rapinchuk
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
Linear algebraic groups with good reduction
Andrei S. Rapinchuk, Igor A. Rapinchuk
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently,…
Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields
Andrei S. Rapinchuk, Igor A. Rapinchuk
We formulate and analyze several finiteness conjectures for linear algebraic groups over higher-dimensional fields. In fact, we prove all of these conjectures for algebraic tori as…
On residue maps for affine curves
Igor A. Rapinchuk
We establish several compatibility results between residue maps in étale and Galois cohomology that arise naturally in the analysis of smooth affine algebraic curves having good re…
On some finiteness results for unramified cohomology
Igor A. Rapinchuk
We obtain several finiteness results for the unramified cohomology of function fields of algebraic varieties defined over fields of type (F'_m), a class that includes algebraically…