论文标题
SemiabelianNéron模型的相对压缩，I
Relative compactifications of semiabelian Néron models, I
论文作者
论文摘要
令$ r $为一个完整的离散估值戒指，$ k（η）$的分数字段，$ s：= {\ rm spec} r $，$（g_η，\ nathcal {l}_η）$ abelian parterian obelian品种$ k（η）$，带有$ \ mathcal {l} $ \ n $ culth $ \ n Mather and $ n Mathron and $ n Mathron $g_η$超过$ s $。假设$ \ MATHCAL {G} $在$ S $上完全退化Semiabelian。然后存在$ \ nathcal {g} $的（p，p，p，p，\ \ \ m rathcal {n}）$，以至于（$α$）$ p $是用cohen-macaulay cohen-macaulay，cohen-macaulay codim $ _p（p \ setminus \ setminus \ natercal {g} $ nible and inter（$β$） $ \ MATHCAL {n} _ {| \ MATHCAL {G}} $ Cubical和$ \ Mathcal {n}_η= \ Mathcal {l}^{\ otimes n}_η$用于某些正整数$ n $。
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 $n$.
