Moduli of Galois p-covers in mixed characteristics

Fix a prime number p. The aim of this paper is to define a complete moduli stack of degree-p covers Y → X , with Y a stable curve which is a G-torsor over X , for a suitable group scheme G/X . The curve X is a twisted curve in the sense of [5, 4] but in general not stable. This follows the same general approach as the characteristic-0 paper [1], but diverges from that of [4], where the curve X is stable, the group scheme G is assumed linearly reductive, but Y is in general much more singular. The approach is based on [12, Proposition 1.2.1] of Raynaud, and the more general notion of effective model of a group-scheme action due to the second author [13]. The general strategy was outlined in [2] in a somewhat special case.