Field of moduli and field of definition of Galois covers

الأصل · EN

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 ₚ that cannot be defined over ₚ, for all primes p>5.