|Title: a-Numbers of curves in Artin–Schreier covers|
|Speaker: Jeremy Booher of University of Arizona|
|Contact: David Zureick-Brown, firstname.lastname@example.org|
|Date: 2019-04-09 at 4:00PM|
|Venue: MSC W201|
Let f : Y -> X be a branched Z/pZ-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 f. 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. This is joint work with Bryden Cais.
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