Éléments explicites en théorie algébrique des nombres

Abstract : 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.
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Stéphane Vinatier. Éléments explicites en théorie algébrique des nombres. Théorie des nombres [math.NT]. Université de Limoges, 2013. ⟨tel-01316937⟩

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