On the degeneration of \'etale $\Bbb Z/p\Bbb Z$ and $\Bbb Z/p^2\Bbb Z$-torsors in equal characteristic$p>0$

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概要

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• 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 \'etale $\Bbb Z/p^n\Bbb Z$-{\it torsor} above the {\it generic} fiber of $X$, for $n=1,2$, with some {\it 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.

• 広島大学の論文

著者

• Mohamed Sa\"{i}di:}}]

  School Of Engineering Computer Sicence And Mathematics University Of Exeter Harrison Building North

関連論文

• On the degeneration of \'etale $\Bbb Z/p\Bbb Z$ and $\Bbb Z/p^2\Bbb Z$-torsors in equal characteristic$p>0$

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