The integral logarithm in Iwasawa theory : an exercise

Jürgen Ritter; Alfred Weiss

doi:10.5802/jtnb.711

The integral logarithm in Iwasawa theory : an exercise

Jürgen Ritter ¹; Alfred Weiss ²

¹ Schnurbeinstraße 14 86391 Deuringen, Germany
² Department of Mathematics University of Alberta Edmonton, AB, Canada T6C 2G1

Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 197-207.

Abstract
Résumé

Let $l$ be an odd prime number and $H$ a finite abelian $l$ -group. We describe the unit group of $Λ_{\land} [H]$ (the completion of the localization at $l$ of $ℤ_{l} [[T]] [H]$ ) as well as the kernel and cokernel of the integral logarithm $L : Λ_{\land} {[H]}^{\times} \to Λ_{\land} [H]$ , which appears in non-commutative Iwasawa theory.

Soient $l$ un nombre premier impair et $H$ un groupe fini abélien. Nous décrivons le groupe d’unités de $Λ_{\land} [H]$ (la complétion du localisé de $ℤ_{l} [[T]] [H]$ en $l$ ) ainsi que le noyau et le conoyau du logarithme intégral $L : Λ_{\land} {[H]}^{\times} \to Λ_{\land} [H]$ , qui apparaît dans la théorie d’Iwasawa non-commutative.

Received: 2007-03-01
Revised: 2007-11-05
Published online: 2010-07-19

MR: 2675880 | Zbl: 1214.11124

DOI: 10.5802/jtnb.711
Author's affiliations:

Jürgen Ritter ¹; Alfred Weiss ²

¹ Schnurbeinstraße 14 86391 Deuringen, Germany
² Department of Mathematics University of Alberta Edmonton, AB, Canada T6C 2G1

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Jürgen Ritter; Alfred Weiss. The integral logarithm in Iwasawa theory : an exercise. Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 197-207. doi : 10.5802/jtnb.711. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.711/

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