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June 2012 Indices Isotypiques des Éléments Cyclotomiques
Tatiana BELIAEVA, Jean-Robert BELLIARD
Tokyo J. Math. 35(1): 139-164 (June 2012). DOI: 10.3836/tjm/1342701348

Abstract

Given $F$ a real abelian field, $p$ an odd prime and $\chi$ any Dirichlet character of $F$, we give a method for computing the $\chi$-index $(H^1(G_S,\mathbf{Z}_p(r))^\chi: C^F(r)^\chi)$ 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 $\chi$-index can now be computed in terms only of elementary arithmetic of finite fields $\mathbf{F}_\ell$. Our work generalizes previous results by Kurihara who used the assumption that the order of $\chi$ divides $p-1$.

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Tatiana BELIAEVA. Jean-Robert BELLIARD. "Indices Isotypiques des Éléments Cyclotomiques." Tokyo J. Math. 35 (1) 139 - 164, June 2012. https://doi.org/10.3836/tjm/1342701348

Information

Published: June 2012
First available in Project Euclid: 19 July 2012

zbMATH: 1255.11055
MathSciNet: MR2977449
Digital Object Identifier: 10.3836/tjm/1342701348

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics

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Vol.35 • No. 1 • June 2012
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