论文标题
伯科维奇曲线上差分形式的减少和提升问题
Reduction and lifting problem for differential forms on Berkovich curves
论文作者
论文摘要
考虑到一个完整的实值$ k $的残留特性零，我们在平滑的$ k $ - 分析曲线$ x $上研究差异形式$ω$的属性。特别是，我们将$（x，ω）$的热带数据和$（x，ω）$与$（x，ω）$的热带数据和代数几何减少数据结合在残基字段$ \ widetilde {k} $上。我们表明，该基准满足了自然兼容性条件，并证明了提升定理的主张，即任何兼容的热带还原基准都可以提升到实际对$ $（x，ω）$。特别是，我们得到了贝恩布里奇，陈，冈德隆，格鲁什夫斯基和莫勒的作品[BCGGM20]的主要结果的简短证明。
Given a complete real-valued field $k$ of residue characteristic zero, we study properties of a differential form $ω$ on a smooth proper $k$-analytic curve $X$. In particular, we associate to $(X,ω)$ a natural tropical reduction datum combining tropical data of $(X,ω)$ and algebra-geometric reduction data over the residue field $\widetilde{k}$. We show that this datum satisfies natural compatibility condition, and prove a lifting theorem asserting that any compatible tropical reduction datum lifts to an actual pair $(X,ω)$. In particular, we obtain a short proof of the main result of a work [BCGGM20] by Bainbridge, Chen, Gendron, Grushevsky, and Möller.
