We study the maximal pseudo-null submodules of Iwasawa modules arising from ideal class groups in -extensions of number fields. We describe several sufficient criteria for the non-triviality of such modules, mainly in dimensions and . 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 -extensions de corps de nombres. Nous décrivons quelques critères de la non-trivialité de ces modules, en nous concentrant sur les cas et . De plus, nous en déduisons des applications à des formes faibles de la conjecture de Greenberg généralisée (GGC).
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Keywords: Greenberg’s Generalised Conjecture, maximal pseudo-null submodules
@article{JTNB_2022__34_2_583_0, author = {Kleine, S\"oren}, 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}, volume = {34}, number = {2}, year = {2022}, doi = {10.5802/jtnb.1218}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.1218/} }
TY - JOUR AU - Kleine, Sören TI - On pseudo-null Iwasawa modules JO - Journal de théorie des nombres de Bordeaux PY - 2022 SP - 583 EP - 618 VL - 34 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.1218/ DO - 10.5802/jtnb.1218 LA - en ID - JTNB_2022__34_2_583_0 ER -
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://www.numdam.org/articles/10.5802/jtnb.1218/
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