Realizing Artin-Schreier covers with minimal a-numbers in positive characteristic
Abstract
Suppose X is a smooth projective connected curve defined over an algebraically closed field of characteristic p > 0 and B subset of X is a finite, possibly empty, set of points. Booher and Cais determined a lower bound for the a-number of a 71/p71-cover of X with branch locus B. For odd primes p, in most cases it is not known if this lower bound is realized. In this note, when X is ordinary, we use formal patching to reduce that question to a computational question about a-numbers of 71/p71-covers of the affine line. As an application, when p = 3 or p = 5, for any ordinary curve X and any choice of B, we prove that the lower bound is realized for Artin-Schreier covers of X with branch locus B. Show more
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Mathematical Sciences PublishersSubject
Artin-Schreier cover; characteristic-p; Cartier operator; p-rank; p-torsion; formal patching; wild ramification; a-number; curve; finite field; Jacobian; arithmetic geometryMore
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