曲线的 $p$-adic 幺模定理
A $p$-adic monodromy theorem for curves
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中文总结 AI 辅助
本文证明 $p$-adic 域上光滑射影曲线的 de Rham $p$-adic 局部系统在有限覆盖拉回后变为半稳定，推广了经典 $p$-adic 幺模定理，并建立了圆盘和环上的相应结果。
中文摘要 AI 辅助
我们证明了 $p$-adic 域上光滑射影曲线上的每个 de Rham $p$-adic 局部系统都是潜在半稳定的；也就是说，沿着曲线的有限覆盖拉回后它变为半稳定。这建立了 Berger 和 André--Kedlaya--Mebkhout 经典 $p$-adic 幺模定理的相对版本。在此过程中，我们还建立了圆盘和环上 de Rham $p$-adic 局部系统的 $p$-adic 幺模定理。
英文摘要
We prove that every de Rham $p$-adic local system on a smooth projective curve over a $p$-adic field is potentially semistable; that is, it becomes semistable after pulling back along a finite cover of the curve. This establishes a relative version of the classical $p$-adic monodromy theorem of Berger and André--Kedlaya--Mebkhout. Along the way, we show that every $p$-adic differential equation near a type I\!V point on a curve becomes trivial after a finite étale extension.
