Dans cette thèse, nous construisons une base du groupe Ck des unités cycolotomiques (au sens de Sinnott) d’une certaine extension abélienne finie k de Q ramifiée exactement sur trois nombres premiers distincts. La première étape consiste en la construction d’une base du goupe Dk des nombres circulaires de k. Par la suite, il sera plus simple d’obtenir une base de Ck. / In this thesis, we construct an explicit basis of the group Ck of cyclotomic units of certain finite abelian extension k of Q ramified at exactly three distinct primes. The first step consists in constructing a basis of the group Dk of circular numbers of k. From there, it is not too difficult to obtain a basis of Ck. The method is combinatorial in nature. We may visualize our construction using a three dimensional cuboid formed of j Gal(k=Q)j small cubes, each of these small cubes containing a Galois conjugate of a primitive circular unit of k. The classical norm relations give rise to some identifications on the cuboid. Using these identifications and an Ennola-type relation (a highly non-trivial relation), we manage to construct an explicit basis of Ck.
| Identifer | oai:union.ndltd.org:LAVAL/oai:corpus.ulaval.ca:20.500.11794/25460 |
| Date | 20 April 2018 |
| Creators | Salami, Azar |
| Contributors | Chapdelaine, Hugo |
| Source Sets | Université Laval |
| Language | English |
| Detected Language | English |
| Type | thèse de doctorat, COAR1_1::Texte::Thèse::Thèse de doctorat |
| Format | 1 ressource en ligne (xxi, 62 pages), application/pdf |
| Rights | http://purl.org/coar/access_right/c_abf2 |
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