Moduli of Galois p-covers in mixed characteristics

Abramovich, Dan; Romagny, Matthieu

doi:10.2140/ant.2012.6.757

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Moduli of Galois $p$-covers in mixed characteristics

Dan Abramovich and Matthieu Romagny

Vol. 6 (2012), No. 4, 757–780

DOI: 10.2140/ant.2012.6.757

Abstract

We define a proper moduli stack classifying covers of curves of prime degree $p$ . The objects of this stack are torsors $Y \to X$ 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

Vol. 6, No. 4, 2012