arXiv subjects

Youness Mazigh

Publications and source records attributed to Youness Mazigh.

4 recordsLinked to original sources

arXiv2019

A genus formula for the positive étale wild kernel

Let $F$ be a number field and let $i\geq 2$ be an integer. In this paper, we study the positive étale wild kernel $\mathrm{WK}^{\mbox{ét},+}_{2i-2}F$, which is the twisted analogue of the $2$-primary part of the narrow class group. If $E/F$ is a Galois extension of number fields with Galois group $G$, we prove a genus formula relating the order of the groups $ (\mathrm{WK}^{\mbox{ét},+}_{2i-2}E)_{G}$ and $\mathrm{WK}^{\mbox{ét},+}_{2i-2}F$.

math.NT↗

arXiv2018

On Iwasawa theory of Rubin-Stark units and narrow class groups

Let $K$ be a totally real number field of degree $r$. Let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{2}$-extension of $K$ and let $L_{\infty}$ be a finite extension of $K_{\infty}$, abelian over $K$. The goal of this paper is to compare the characteristic ideal of the $χ$-quotient of the projective limit of the narrow class groups to the $χ$-quotient of the projective limit of the $r$-th exterior power of totally positive units modulo a subgroup of Rubin-Stark units, for some $\overline{\mathbb{Q}_{2}}$-irreducible characters $χ$ of $\mathrm{Gal}(L_{\infty}/K_{\infty})$.

math.NT↗

arXiv2017

The index of Rubin-Stark units

The aim of this paper is to compare the orders of the class groups and the quotients of the $r$-th exterior power of units modulo Rubin-Stark units.

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arXiv2016

Iwasawa theory of Rubin-Stark units and class group

Let $K$ be a totally real number field of degree $r=[K:\mathbb{Q}]$ and let $p$ be an odd rational prime. Let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{p}$-extension of $K$ and let $L_{\infty}$ be a finite extension of $K_{\infty}$, abelian over $K$. In this article, we extend results of \cite{Kazim109} relating characteristic ideal of the $χ$-quotient of the projective limit of the ideal class groups to the $χ$-quotient of the projective limit of the $r$-th exterior power of units modulo Rubin-Stark units, in the non semi-simple case, for some $\overline{\mathbb{Q}_{p}}$-irreductible characters $χ$ of $\mathrm{Gal}(L_{\infty}/K_{\infty})$.

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