Tamely Ramified Morphisms of Curves and Belyi’s Theorem in Positive Characteristic

Kiran S. Kedlaya, Daniel Litt, Jakub Witaszek

Research output: Contribution to journalArticlepeer-review

Abstract

We show that every smooth projective curve over a finite field k admits a finite tame morphism to the projective line over k. Furthermore, we construct a curve with no such map when k is 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.

Original languageEnglish (US)
Pages (from-to)2803-2833
Number of pages31
JournalInternational Mathematics Research Notices
Volume2023
Issue number4
DOIs
StatePublished - Feb 1 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics

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