Néron models, minimal models, and birational group actions

János Kollár

paper

Néron models, minimal models, and birational group actions

arXiv:2502.13800

Abstract

Let $A_{K}$ be an Abelian variety over the quotient field of a Dedekind domain $R$ . We show that the identity component of the Néron model of $A_{K}$ acts regularly on any minimal model of $A_{K}$ over $R$ , and discuss when the Néron 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.