Vol. 6, No. 4, 2012

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Moduli of Galois $p$-covers in mixed characteristics

Dan Abramovich and Matthieu Romagny

Vol. 6 (2012), No. 4, 757–780
Abstract

We define a proper moduli stack classifying covers of curves of prime degree p. The objects of this stack are torsors Y X under a finite flat X-group scheme, with X a twisted curve and Y a stable curve. We also discuss embeddings of finite flat group schemes of order p into affine smooth 1-dimensional group schemes.

Keywords
curves, group schemes of order $p$, moduli
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14L15
Milestones
Received: 26 February 2011
Revised: 11 June 2011
Accepted: 17 July 2011
Published: 25 July 2012
Authors
Dan Abramovich
Department of Mathematics
Brown University
Box 1917
151 Thayer Street
Providence, RI 02912
United States
Matthieu Romagny
Université Pierre et Marie Curie (Paris 6)
4 place Jussieu
F-75252 Paris
France