La recherche

For a fixed finite group G, we study the fields of definition of geometrically irreducible components of Hurwitz moduli schemes of marked branched G-covers of the projective line. The main focus is on determining whether components obtained by "gluing" two other components, both defined over a number field K, are also defined over K. The article presents a list of situations in which a positive answer is obtained. As an application, when G is a semi-direct product of symmetric groups or the Mathieu group M 23 , components defined over Q of small dimension (6 and 4, respectively) are shown to exist.

Quelques aspects de l’élaboration de l’analyse fonctionnelle jusqu’à Banach. Rôle des opérations dans une approche générale