A-numbers of curves in Artin–Schreier covers

Jeremy Booher, Bryden Cais

Research output: Contribution to journalArticle

Abstract

Let π: 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 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.

Original languageEnglish (US)
Pages (from-to)587-641
Number of pages55
JournalAlgebra and Number Theory
Volume14
Issue number3
DOIs
StatePublished - 2020

Keywords

  • A-numbers
  • Arithmetic geometry
  • Artin–Schreier covers
  • Covers of curves
  • Invariants of curves

ASJC Scopus subject areas

  • Algebra and Number Theory

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