Unités de Stark et théorie d'Iwasawa

Abstract : In this thesis, we construct Euler systems coming from the (conjectural) Stark units and those of Rubin-Stark of a number field K, to describe the characteristic ideal of the X-quotient of the standard Iwasawa module X∞, for some p-adic irreducible characters X. Here X∞ is the Galois group of the maximal unramified abelian pro-p-extension of K∞, where K∞ is an adequate Zp-extension of K. Precisely, we demonstrate a divisibility results formulated by the main conjecture of Iwasawa theory. Our demonstrations essentially are based on the theory of Euler systems.
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Youness Mazigh. Unités de Stark et théorie d'Iwasawa. Théorie des nombres [math.NT]. Université Bourgogne Franche-Comté, 2017. Français. 〈NNT : 2017UBFCD005〉. 〈tel-01795150〉

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