Tamely Ramified Morphisms of Curves and Belyi’s Theorem in Positive Characteristic
Tamely Ramified Morphisms of Curves and Belyi’s Theorem in Positive Characteristic
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曲线的驯化分支态射与正特征中的Beyi’s定理
DOI：
10.1093/imrn/rnab309
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发表时间：
2021
影响因子：
1
通讯作者：
Witaszek, Jakub
中科院分区：
文献类型：
--
作者：
Kedlaya, Kiran S.;Litt, Daniel;Witaszek, Jakub
我们证明了有限域上的每条平滑射影曲线都承认射影线具有有限的驯服态射。此外，当 是特征二的无限完美域时，我们构造了一条没有这样的映射的曲线。我们的工作以 Saïdi、Sugiyama-Yasuda 和 Anbar-Tutdere 的结果为基础，对温和的 Belyi 定理进行了积极的改进。
We show that every smooth projective curve over a finite fieldadmits a finite tame morphism to the projective line over. Furthermore, we construct a curve with no such map whenis an infinite perfect field of characteristic two. Our work leads to a refinement of the tame Belyi theorem in positive characteristic, building on results of Saïdi, Sugiyama–Yasuda, and Anbar–Tutdere.