On pseudo-null Iwasawa modules

Sören Kleine

doi:10.5802/jtnb.1218

Sören Kleine ¹

¹ Institut für Theoretische Informatik, Mathematik und Operations Research Universität der Bundeswehr München Werner-Heisenberg-Weg 39 D-85577 Neubiberg, Germany

Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 2, pp. 583-618.

Résumé
Abstract

Nous étudions les sous-modules pseudo-nuls maximaux de certains modules d’Iwasawa construits à partir des groupes de classes d’idéaux dans des $ℤ_{p}^{k}$ -extensions de corps de nombres. Nous décrivons quelques critères de la non-trivialité de ces modules, en nous concentrant sur les cas $k = 1$ et $k = 2$ . De plus, nous en déduisons des applications à des formes faibles de la conjecture de Greenberg généralisée (GGC).

We study the maximal pseudo-null submodules of Iwasawa modules arising from ideal class groups in $ℤ_{p}^{k}$ -extensions of number fields. We describe several sufficient criteria for the non-triviality of such modules, mainly in dimensions $k = 1$ and $k = 2$ . This has applications to weak versions of Greenberg’s Generalised Conjecture (GGC).

Reçu le : 2021-02-26
Révisé le : 2021-07-02
Accepté le : 2021-11-11
Publié le : 2022-10-24

DOI : 10.5802/jtnb.1218

Classification : 11R23
Mots clés : Greenberg’s Generalised Conjecture, maximal pseudo-null submodules

Affiliations des auteurs :

Sören Kleine ¹

¹ Institut für Theoretische Informatik, Mathematik und Operations Research Universität der Bundeswehr München Werner-Heisenberg-Weg 39 D-85577 Neubiberg, Germany

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On pseudo-null {Iwasawa} modules},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {583--618},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
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Sören Kleine. On pseudo-null Iwasawa modules. Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 2, pp. 583-618. doi : 10.5802/jtnb.1218. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1218/

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