论文标题
Raynaud定理的算术变体
An arithmetic variant of Raynaud's theorem
论文作者
论文摘要
众所周知，对于常规的可半固定曲线$ \ mathfrak x $，在DVR上具有代数封闭的残留场，$ \ mathfrak x $的双纤维的双图的跨越树木均与jacobian型号的特殊纤维的组成部分，该组件是$ \ mathfrak x $的Néron模型的特殊纤维。我们证明了这一事实的概括，该事实不需要使用双图的组合版本来编码有关$ \ Mathfrak x $上的分隔线的算术信息，因此不需要将残基字段封闭。
It is well known that for a regular semistable curve $\mathfrak X$ over a DVR with algebraically closed residue field, the spanning trees of the dual graph of the special fiber of $\mathfrak X$ are in bijection with components of the special fiber of the Néron model of the Jacobian of $\mathfrak X$. We prove a generalization of this fact that does not require the residue field to be algebraically closed, using a combinatorially enriched version of the dual graph to encode arithmetic information about divisors on $\mathfrak X$.
