Ordinary and supersingular covers in characteristic p

David Harbater

Vol. 113 (1984), No. 2, 349–363

DOI: 10.2140/pjm.1984.113.349

Abstract

This paper studies Galois wildly ramified covers of the projective line in characteristic p. It is shown that for p-covers of tamely ramified covers, the monodromy is “generated by the branch cycles.” But examples are given to show that this condition fails in general for towers taken in the opposite order and for other covers as well—even in the case of covers branched only over infinity. It is also shown that p-covers branched at a single point are supersingular and more generally that for any curve which arises as a p-cover, there is a bound on the p-rank which in general is less than the genus.

Mathematical Subject Classification 2000

Primary: 14H30

Secondary: 14E20, 14E22

Milestones

Received: 13 December 1982

Revised: 19 April 1983

Published: 1 August 1984