Néron models, minimal models, and birational group actions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917929321234432 |
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| author | Kollár, János |
| author_facet | Kollár, János |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Néron models, minimal models, and birational group actions Kollár, János Algebraic Geometry Number Theory 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. |
| title | Néron models, minimal models, and birational group actions |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2502.13800 |