Algebra & Number Theory
- Algebra Number Theory
- Volume 14, Number 3 (2020), 587-641.
$a$-numbers of curves in Artin–Schreier covers
Let be a branched -cover of smooth, projective, geometrically connected curves over a perfect field of characteristic . We investigate the relationship between the -numbers of and and the ramification of the map . This is analogous to the relationship between the genus (respectively -rank) of and given the Riemann–Hurwitz (respectively Deuring–Shafarevich) formula. Except in special situations, the -number of is not determined by the -number of and the ramification of the cover, so we instead give bounds on the -number of . We provide examples showing our bounds are sharp. The bounds come from a detailed analysis of the kernel of the Cartier operator.
Algebra Number Theory, Volume 14, Number 3 (2020), 587-641.
Received: 26 July 2018
Revised: 2 September 2019
Accepted: 7 October 2019
First available in Project Euclid: 2 July 2020
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Booher, Jeremy; Cais, Bryden. $a$-numbers of curves in Artin–Schreier covers. Algebra Number Theory 14 (2020), no. 3, 587--641. doi:10.2140/ant.2020.14.587. https://projecteuclid.org/euclid.ant/1593655266