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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.08113 |
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| _version_ | 1866916317820354560 |
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| author | Mitsui, Kentaro Nakamura, Iku |
| author_facet | Mitsui, Kentaro 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 $\mathcal{L}_η$ ample cubical and $\mathcal{G}$ the Néron model of $G_η$ over $S$. Suppose that $\mathcal{G}$ is totally degenerate semiabelian over $S$. Then there exists a (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 $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08113 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Relative compactifications of semiabelian Néron models, I Mitsui, Kentaro 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 $\mathcal{L}_η$ ample cubical and $\mathcal{G}$ the Néron model of $G_η$ over $S$. Suppose that $\mathcal{G}$ is totally degenerate semiabelian over $S$. Then there exists a (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 $n$. |
| title | Relative compactifications of semiabelian Néron models, I |
| topic | Algebraic Geometry Primary 14K05, Secondary 14J10, 14K99 |
| url | https://arxiv.org/abs/2201.08113 |