Raynaud-Tamagawa theta divisors and new-ordinariness of ramified coverings of curves

Abstract

Let (X,DX) be a smooth pointed stable curve over an algebraically closed field k of characteristic p>0. Suppose that (X,DX) is generic. We give a necessary and sufficient condition for new-ordinariness of prime-to-p cyclic tame coverings of (X,DX). This result generalizes a result of S. Nakajima concerning the ordinariness of prime-to-p cyclic étale coverings of generic curves to the case of tamely ramified coverings.