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Jordan property for groups of birational selfmaps
- Part of
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 12 / December 2014
- Published online by Cambridge University Press:
- 17 September 2014, pp. 2054-2072
- Print publication:
- December 2014
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- Article
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- You have access
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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.
