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Soit un revêtement de la droite projective défini sur , de groupe
de monodromie . Soit le compositum des corps de rationalité des points de
branchement , et le corps des modules correspondants. Partant du lien entre corps
des modules et espaces de Hurwitz, on étudie la géométrie et l’arithmétique de ces
espaces et des espaces de configuration de points complétés pour évaluer la ramification
dans des mauvaises places de qui ne divisent pas l’ordre de , mais où les
points de branchements...
This article provides necessary and sufficient conditions for each group of order 32 to be realizable as a Galois group over an arbitrary field. These conditions, given in terms of the number of square classes of the field and the triviality of specific elements in related Brauer groups, are used to derive a variety of automatic realizability results.
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