On pseudo-null Iwasawa modules
Journal de théorie des nombres de Bordeaux, Volume 34 (2022) no. 2, pp. 583-618.

We study the maximal pseudo-null submodules of Iwasawa modules arising from ideal class groups in 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).

Nous étudions les sous-modules pseudo-nuls maximaux de certains modules d’Iwasawa construits à partir des groupes de classes d’idéaux dans des 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).

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1218
Classification: 11R23
Keywords: Greenberg’s Generalised Conjecture, maximal pseudo-null submodules
Kleine, Sören 1

1 Institut für Theoretische Informatik, Mathematik und Operations Research Universität der Bundeswehr München Werner-Heisenberg-Weg 39 D-85577 Neubiberg, Germany
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Kleine, Sören. On pseudo-null Iwasawa modules. Journal de théorie des nombres de Bordeaux, Volume 34 (2022) no. 2, pp. 583-618. doi : 10.5802/jtnb.1218. http://archive.numdam.org/articles/10.5802/jtnb.1218/

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