English

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

Algebraic Geometry 2025-02-20 v1 Number Theory

Abstract

Let AKA_K be an Abelian variety over the quotient field of a Dedekind domain RR. We show that the identity component of the N\'eron model of AKA_K acts regularly on any minimal model of AKA_K over RR, 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.

Keywords

Cite

@article{arxiv.2502.13800,
  title  = {N\'eron models, minimal models, and birational group actions},
  author = {János Kollár},
  journal= {arXiv preprint arXiv:2502.13800},
  year   = {2025}
}
R2 v1 2026-06-28T21:50:11.102Z