On genus change in algebraic curves over imperfect fields

Schröer, Stefan

doi:10.1090/S0002-9939-08-09712-8

On genus change in algebraic curves over imperfect fields
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Proc. Amer. Math. Soc. 137 (2009), 1239-1243 Request permission

Abstract:

We give a new proof, in scheme-theoretic language, of Tate’s classical result on genus change of curves over imperfect fields in characteristic $p>0$. Namely, for normal geometrically integral curves, the difference between arithmetic and geometric genus over the algebraic closure is divisible by $(p-1)/2$.

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