Stéphane Vinatier (research)

Habilitation à diriger des recherches

Explicit elements in algebraic number theory, University of Limoges (2013) [pdf] ;
defended 9th of december 2013 in front of Ph. Cassou-Noguès (Université de Bordeaux, President, referee), C. Greither (Universität der Bundeswehr München, referee), F. Laubie (Université de Limoges), S. Louboutin (Aix-Marseille Université, referee), C. Maire (Université de Franche-Comté) et A. Salinier (Université de Limoges)

This report consists in a synthesis of my research activities in algebraic number theory, between 2003 and 2013, on my own or with colleagues. The main goal is the study of the Galois module structure of modules associated to number field extensions, under various hypothesis, specifically about ramification. We also present results about other subjects which came into the way of the previous study: the construction of a certain type of Galois extensions of the field of rationals, the complexity of self-dual normal bases for multiplication in finite fields, and a bit of combinatorics. We stress the importance of an explicit knowledge of the objects under study.

Galois module structure, ramification, number fields, Gauss sums, resolvants, self-dual normal bases.