Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields
Number Theory
2020-02-18 v2 Algebraic Geometry
Group Theory
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.
Keywords
Cite
@article{arxiv.2002.01520,
title = {Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields},
author = {Andrei S. Rapinchuk and Igor A. Rapinchuk},
journal= {arXiv preprint arXiv:2002.01520},
year = {2020}
}
Comments
Besides minor changes in exposition, we have added a new adelic proof of Theorem 1.2. This, in particular, allows us to remove any restrictions on the characteristic of the field