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2020 $a$-numbers of curves in Artin–Schreier covers
Jeremy Booher, Bryden Cais
Algebra Number Theory 14(3): 587-641 (2020). DOI: 10.2140/ant.2020.14.587

Abstract

Let π:YX be a branched ZpZ-cover of smooth, projective, geometrically connected curves over a perfect field of characteristic p>0. We investigate the relationship between the a-numbers of Y and X and the ramification of the map π. This is analogous to the relationship between the genus (respectively p-rank) of Y and X given the Riemann–Hurwitz (respectively Deuring–Shafarevich) formula. Except in special situations, the a-number of Y is not determined by the a-number of X and the ramification of the cover, so we instead give bounds on the a-number of Y. We provide examples showing our bounds are sharp. The bounds come from a detailed analysis of the kernel of the Cartier operator.

Citation

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Jeremy Booher. Bryden Cais. "$a$-numbers of curves in Artin–Schreier covers." Algebra Number Theory 14 (3) 587 - 641, 2020. https://doi.org/10.2140/ant.2020.14.587

Information

Received: 26 July 2018; Revised: 2 September 2019; Accepted: 7 October 2019; Published: 2020
First available in Project Euclid: 2 July 2020

MathSciNet: MR4113776
Digital Object Identifier: 10.2140/ant.2020.14.587

Subjects:
Primary: 14G17
Secondary: 11G20, 14H40

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2020
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