Jordan property for groups of birational selfmaps
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- 17 September 2014
- journal article
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 150 (12) , 2054-2072
Abstract
Assuming a particular case of the Borisov–Alexeev–Borisov conjecture, we prove that finite subgroups of the automorphism group of a finitely generated field over $\mathbb{Q}$ have bounded orders. Further, we investigate which algebraic varieties have groups of birational selfmaps satisfying the Jordan property. Unless explicitly stated otherwise, all varieties are assumed to be algebraic, geometrically irreducible and defined over an arbitrary field $\Bbbk$ of characteristic zero.
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