Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields

2020/02/04 by Rapinchuk, Andrei S., Rapinchuk, Igor A.
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2002.01520

Abstract

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 well as in some other situations. This work relies in an essential way on several finiteness results for unramified cohomology.

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