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arXiv · 0912.0819

Indices isotypiques des éléments cyclotomiques

Tatiana Beliaeva·Jean-Robert Belliard
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Abstract

Given $F$ a real abelian field, $p$ an odd prime and $χ$ any Dirichlet character of $F$ we give a method for computing the $χ$-index $\displaystyle (H^1(G_S,\mathbb{Z}_p(r))^χ: C^F(r)^χ)$ where the Tate twist $r$ is an odd integer $r\geq 3$, the group $C^F(r)$ is the group of higher circular units, $G_S$ is the Galois group over $F$ of the maximal $S$ ramified algebraic extension of $F$, and $S$ is the set of places of $F$ dividing $p$. This $χ$-index can now be computed in terms only of elementary arithmetic of finite fields $\FM_\ell$. Our work generalizes previous results by Kurihara who used the assumption that the order of $χ$ divides $p-1$.

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Tatiana Beliaeva, Jean-Robert Belliard. 2011-12-15. Indices isotypiques des éléments cyclotomiques. https://arxiv.org/abs/0912.0819

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