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July 2007 On the degeneration of étale $\Bbb Z/p\Bbb Z$ and $\Bbb Z/p^2\Bbb Z$-torsors in equal characteristic $p>0$
Mohamed Saïdi
Hiroshima Math. J. 37(2): 315-341 (July 2007). DOI: 10.32917/hmj/1187916322

Abstract

Let $R$ be a complete discrete valuation ring of equal characteristic $p>0$. In this paper we investigate finite and flat morphisms $f:Y\to X$ between formal $R$-schemes which have the structure of an étale $\Bbb Z/p^n\Bbb Z$-torsor above the generic fiber of $X$, for $n=1,2$, with some extra geometric conditions on $X$ and $Y$. In the case $n=1$, we prove that $f$ has the structure of a torsor under a finite and flat $R$-group scheme of rank $p$ and we describe the group schemes that arise as the group of the torsor. In the case $n=2$, we describe explicitly how the Artin-Schreier-Witt equations describing $f$ on the generic fiber, locally, degenerate. Moreover, in some cases where $f$ has the structure of a torsor under a finite and flat $R$-group scheme of rank $p^2$, we describe the group schemes of rank $p^2$ which arise in this way.

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Mohamed Saïdi. "On the degeneration of étale $\Bbb Z/p\Bbb Z$ and $\Bbb Z/p^2\Bbb Z$-torsors in equal characteristic $p>0$." Hiroshima Math. J. 37 (2) 315 - 341, July 2007. https://doi.org/10.32917/hmj/1187916322

Information

Published: July 2007
First available in Project Euclid: 24 August 2007

zbMATH: 1155.14025
MathSciNet: MR2345371
Digital Object Identifier: 10.32917/hmj/1187916322

Subjects:
Primary: 14D06, 14D15, 14E20, 14H30

Rights: Copyright © 2007 Hiroshima University, Mathematics Program

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Vol.37 • No. 2 • July 2007
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