Tamely ramified morphisms of curves
--  Kiran Kedlaya, February 22, 2019

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For a curve over a field of characteristic not equal to 2, it is easy to
produce finite separable morphisms to the projective line which have
only simple branching, and hence are everywhere tamely ramified. In
characteristic 2, the existence of a tamely ramified morphism is a much
subtler question. Building on work of Schroeer, Sugiyama-Yasuda, and
Anbar-Tutdere, we identify a Brauer obstruction to the existence of such
a morphism on one hand, and the other hand show that such morphisms
always exist when the base field is algebraically closed (by
Sugiyama-Yasuda) or finite (a new result). We also describe consequences
for the tame Belyi theorem in characteristic 2. Joint work with Daniel
Litt and Jakub Witaszek.