Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2405.09172 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910521082511360 |
|---|---|
| author | Nakamura, Iku |
| author_facet | Nakamura, Iku |
| contents | Let $R$ be a complete discrete valuation ring, $k(η)$ its fraction field, $S={\rm Spec} R$, $(G_η,\mathcal{L}_η)$ a polarized abelian variety over $k(η)$ with $\mathcal{L}_η$ symmetric ample cubical and $\mathcal{G}$ the Néron model of $G_η$ over $S$. Suppose that $\mathcal{G}$ is semiabelian over $S$. Then there exists a {\it unique} relative compactification $(P,\mathcal{N})$ of $\mathcal{G}$ such that ($α$) $P$ is Cohen-Macaulay with codim$_P(P\setminus\mathcal{G})=2$ and ($β$) $\mathcal{N}$ is ample invertible with $\mathcal{N}_{|\mathcal{G}}$ cubical and $\mathcal{N}_η = \mathcal{L}^{\otimes n}_η$ for some positive integer $n$. The totally degenerate case has been studied in \cite{MN24}. We discuss here first the partially degenerate case and then the case where $R$ is a Dedekind domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09172 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative compactification of semiabelian Néron models, II Nakamura, Iku Algebraic Geometry Primary 14K05, Secondary 14J10, 14K99 Let $R$ be a complete discrete valuation ring, $k(η)$ its fraction field, $S={\rm Spec} R$, $(G_η,\mathcal{L}_η)$ a polarized abelian variety over $k(η)$ with $\mathcal{L}_η$ symmetric ample cubical and $\mathcal{G}$ the Néron model of $G_η$ over $S$. Suppose that $\mathcal{G}$ is semiabelian over $S$. Then there exists a {\it unique} relative compactification $(P,\mathcal{N})$ of $\mathcal{G}$ such that ($α$) $P$ is Cohen-Macaulay with codim$_P(P\setminus\mathcal{G})=2$ and ($β$) $\mathcal{N}$ is ample invertible with $\mathcal{N}_{|\mathcal{G}}$ cubical and $\mathcal{N}_η = \mathcal{L}^{\otimes n}_η$ for some positive integer $n$. The totally degenerate case has been studied in \cite{MN24}. We discuss here first the partially degenerate case and then the case where $R$ is a Dedekind domain. |
| title | Relative compactification of semiabelian Néron models, II |
| topic | Algebraic Geometry Primary 14K05, Secondary 14J10, 14K99 |
| url | https://arxiv.org/abs/2405.09172 |