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arXiv · 2502.13800

N\'eron models, minimal models, and birational group actions

János Kollár
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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 N\'eron model of $A_K$ acts regularly on any minimal model of $A_K$ 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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János Kollár. 2025-02-19. N\'eron models, minimal models, and birational group actions. https://arxiv.org/abs/2502.13800

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