Some remarks on pseudo-null submodules of tamely ramified Iwasawa modules
Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 533-555.

Nous donnons diverses observations sur la structure des modules d’Iwasawa modérément ramifiés pour une p -extension (ou une p -extension multiple) d’un corps de nombres. Dans cet article, nous considérons la question de savoir si un module d’Iwasawa modérément ramifié possède un sous-module fini (ou pseudo-nul) non-nul ou non. Pour la p -extension cyclotomique de (avec p impair), nous pouvons obtenir une solution complète à cette question. Nous donnons également des conditions suffisantes pour avoir un sous-module pseudo-nul non-nul pour la p 2 -extension d’un corps quadratique imaginaire. Et nous donnons aussi une application de nos résultats à la « théorie d’Iwasawa non-abélienne » dans le sens d’Ozaki.

We will give several observations about the structure of tamely ramified Iwasawa modules for a p -extension (or a multiple p -extension) of an algebraic number field. In the present paper, we consider the question whether a given tamely ramified Iwasawa module has a non-trivial finite (or pseudo-null) submodule or not. For the cyclotomic p -extension of (with odd p), we can obtain a complete answer to this question. We also give sufficient conditions for having a non-trivial pseudo-null submodule for the case of the p 2 -extension of an imaginary quadratic field. We also give an application of our results to the “non-abelian Iwasawa theory” in the sense of Ozaki.

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DOI : https://doi.org/10.5802/jtnb.1038
Classification : 11R23
Mots clés : Iwasawa modules, finite submodules, pseudo-null submodules
@article{JTNB_2018__30_2_533_0,
     author = {Fujii, Satoshi and Itoh, Tsuyoshi},
     title = {Some remarks on pseudo-null submodules of tamely ramified Iwasawa modules},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {533--555},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {30},
     number = {2},
     year = {2018},
     doi = {10.5802/jtnb.1038},
     zbl = {1442.11144},
     mrnumber = {3891326},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jtnb.1038/}
}
Fujii, Satoshi; Itoh, Tsuyoshi. Some remarks on pseudo-null submodules of tamely ramified Iwasawa modules. Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 533-555. doi : 10.5802/jtnb.1038. http://archive.numdam.org/articles/10.5802/jtnb.1038/

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