Fake liftings of Galois covers between smooth curves
Saidi, M
Date: 1 December 2012
Publisher
Mathematical Society of Japan / World Scientific Publishing Company
Publisher DOI
Abstract
In this paper we investigate the problem of lifting of Galois covers between algebraic curves from characteristic p > 0 to characteristic 0. We prove a
refined version of the main result of Garuti concerning this problem in [Ga]. We
formulate a refined version of the Oort conjecture on liftings of cyclic Galois covers
between curves. ...
In this paper we investigate the problem of lifting of Galois covers between algebraic curves from characteristic p > 0 to characteristic 0. We prove a
refined version of the main result of Garuti concerning this problem in [Ga]. We
formulate a refined version of the Oort conjecture on liftings of cyclic Galois covers
between curves. We introduce the notion of fake liftings of cyclic Galois covers between curves, their existence would contradict the Oort conjecture, and we study the
geometry of their semi-stable models. Finally, we introduce and investigate on some
examples the smoothening process, which ultimately aims to show that fake liftings
do not exist. This in turn would imply the Oort conjecture.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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