Field of moduli and field of definition of Galois covers

2001/08/01 by Stefan Wewers, Wewers, Stefan
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paper · pdf · doi:10.48550/arxiv.math/0108003

25 pages, 2 figures; to appear in "Arithmetic fundamental groups and Noncommutative algebra"

arxiv created 2001/08/01 · openalex publication_date 2001/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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