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Field of moduli and field of definition of Galois covers

Stefan Wewers
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Abstract

In this paper we investigate the cohomological obstruction for the field of moduli of a $G$-cover to be a field of definition, in the case of local fields and covers with tame admissible reduction. This applies in particular to $p$-adic fields where $p$ does not divide the order of the group $G$. We give examples of $G$-covers with field of moduli $\QQ_p$ that cannot be defined over $\QQ_p$, for all primes $p>5$.

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Stefan Wewers. 2001-08-01. Field of moduli and field of definition of Galois covers. https://arxiv.org/abs/math/0108003

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