N\'eron models, minimal models, and birational group actions
Abstract
Let AK be an Abelian variety over the quotient field of a Dedekind domain R. We show that the identity component of the N\'eron model of AK acts regularly on any minimal model of AK over R, and discuss when the N\'eron model is an open subset of a minimal model. The main technical result is the rigidity of small modifications, leading to a regularity criterion for birational group actions.
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