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arXiv · 1904.04070

A genus formula for the positive \'{e}tale wild kernel

Hassan Asensouyis·Jilali Assim·Youness Mazigh
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Abstract

Let $F$ be a number field and let $i\geq 2$ be an integer. In this paper, we study the positive \'{e}tale wild kernel $\mathrm{WK}^{\mbox{\'{e}t},+}_{2i-2}F$, 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{\'{e}t},+}_{2i-2}E)_{G}$ and $\mathrm{WK}^{\mbox{\'{e}t},+}_{2i-2}F$.

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BibTeXRIS

Hassan Asensouyis, Jilali Assim, Youness Mazigh. 2019-04-08. A genus formula for the positive \'{e}tale wild kernel. https://arxiv.org/abs/1904.04070

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