@article{a36b98033cd14038880b40cce039d7ec,
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.",
author = "Kedlaya, {Kiran S.} and Daniel Litt and Jakub Witaszek",
note = "Funding Information: Thanks to Seichi Yasuda for directing us to Hoshi{\textquoteright}s work on the Schwarzian derivative and to Piotr Achinger and Maciej Zdanowicz for helpful comments. We thank the referee for their suggestions and for reading the article carefully. This paper began while all three authors were at the IAS for the 2018–2019 academic year, supported by a visiting professorship (Kedlaya) and NSF grant DMS-1638352 (Litt, Witaszek). Kedlaya and Witaszek also visited MSRI (NSF grant DMS-1440140) during spring 2019. Kedlaya was additionally supported by NSF (grants DMS-1501214, DMS-1802161) and UCSD (Warschawski Professorship). Litt was additionally supported by NSF grant DMS-2001196. Witaszek was additionally supported by NSF grant DMS-2101897. Publisher Copyright: {\textcopyright} The Author(s) 2021. Published by Oxford University Press. All rights reserved.",
year = "2023",
month = feb,
day = "1",
doi = "10.1093/imrn/rnab309",
language = "English (US)",
volume = "2023",
pages = "2803--2833",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "4",
}