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 ; Alfred Weiss

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

Résumé
Abstract

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.

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.

Reçu le : 2007-03-01
Révisé le : 2007-11-05
Publié le : 2010-07-19

MR 2675880 | Zbl 1214.11124

DOI : https://doi.org/10.5802/jtnb.711

@article{JTNB_2010__22_1_197_0,
     author = {J\"urgen Ritter and Alfred Weiss},
     title = {The integral logarithm in {Iwasawa} theory~: an exercise},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {197--207},
     publisher = {Universit\'e Bordeaux 1},
     volume = {22},
     number = {1},
     year = {2010},
     doi = {10.5802/jtnb.711},
     zbl = {1214.11124},
     mrnumber = {2675880},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.711/}
}

Jürgen Ritter; Alfred Weiss. The integral logarithm in Iwasawa theory : an exercise. Journal de Théorie des Nombres de Bordeaux, Tome 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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