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| HAL: hal-00438674, version 2 |
| arXiv: 0912.0819 |
| Detailed view |  Export this paper |
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| Available versions: | v2 (2011-12-15) |
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| Indices isotypiques des éléments cyclotomiques. |
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Tatiana Beliaeva 1Jean-Robert Belliard 2, 3 |
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| (2009-12-04) |
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| 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 $\displaystyle \left (H^1(G_S,\mathbb{Z}_p(r))^\chi: C^F(r)^\chi\right)$ 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 $\FM_\ell$. Our work generalizes previous results by Kurihara who used the assumption that the order of $\chi$ divides $p-1$. |
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| 1: | Institut de Recherche Mathématique Avancée (IRMA) |
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CNRS : UMR7501 – Université de Strasbourg |
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| 2: | Laboratoire de Mathématiques (LM-Besançon) |
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CNRS : UMR6623 – Université de Franche-Comté |
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| 3: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Subject | : | Mathematics/Number Theory |
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| Galois cohomologie – Iwasawa theory – cyclotomic fields. |
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| hal-00438674, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00438674 | |
| oai:hal.archives-ouvertes.fr:hal-00438674 | |
| From: Jean-Robert Belliard | |
| Submitted on: Thursday, 15 December 2011 10:52:49 | |
| Updated on: Thursday, 15 December 2011 14:24:56 | |
