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 $Y\to \mathsc{X}$ under a finite flat $\mathsc{X}$-group scheme, with $\mathsc{X}$ 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
Primary: 14H10
Secondary: 14L15