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