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

Kiran S. Kedlaya; Daniel Litt; Jakub Witaszek

doi:10.1093/imrn/rnab309

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

Kiran S. Kedlaya, Daniel Litt, Jakub Witaszek

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	2803-2833
Number of pages	31
Journal	International Mathematics Research Notices
Volume	2023
Issue number	4
DOIs	https://doi.org/10.1093/imrn/rnab309
State	Published - Feb 1 2023
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnab309

Cite this

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title = "Tamely Ramified Morphisms of Curves and Belyi{\textquoteright}s Theorem in Positive Characteristic",

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 Sa{\"i}di, Sugiyama–Yasuda, and Anbar–Tutdere.",

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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