Néron models, minimal models, and birational group actions

János Kollár

doi:10.4310/PAMQ.250430140912

Néron models, minimal models, and birational group actions

János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

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 Spec 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.

Original language	English (US)
Pages (from-to)	647-673
Number of pages	27
Journal	Pure and Applied Mathematics Quarterly
Volume	22
Issue number	2
DOIs	https://doi.org/10.4310/PAMQ.250430140912
State	Published - 2026

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4310/PAMQ.250430140912

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title = "N{\'e}ron 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{\'e}ron model of AK acts regularly on any minimal model of AK over Spec R, and discuss when the N{\'e}ron 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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AB - Let AK be an Abelian variety over the quotient field of a Dedekind domain R. We show that the identity component of the Néron model of AK acts regularly on any minimal model of AK over Spec 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.

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M3 - Article

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JO - Pure and Applied Mathematics Quarterly

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Néron models, minimal models, and birational group actions

Abstract

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