Finite Λ-submodules of Iwasawa modules for a CM-field for p=2
Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 1017-1035.

Soit F un corps CM et p un nombre premier. Soit X F - le quotient “moins” du groupe de Galois de la pro-p-extension abélienne non ramifiée maximale de la p -extension cyclotomique de F. Si p ne vaut pas 2, il est bien connu que X F - n’a pas de sous-module fini non-trivial. Mais pour p=2, il peut arriver que X F - contient un sous-module fini non-trivial. Dans cet article, nous étudions le sous-module fini maximal de X F - pour p=2, et nous déterminons ce module sous certaines légères hypothèses.

Let p be a prime, X F - the minus quotient of the Iwasawa module, which we define to be the Galois group of the maximal unramified abelian pro-p-extension over the cyclotomic p -extension over a CM field F. If p is an odd prime, it is well known that X F - has no non-trivial finite p Gal(F /F)-submodule. But X F - has non-trivial finite p Gal(F /F)-submodule in some cases for p=2. In this paper, we study the maximal finite p Gal(F /F)-submodule of X F - for p=2. We determine the size of the maximal finite 2 Gal(F /F)-submodule of X F - under some mild assumptions.

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DOI : https://doi.org/10.5802/jtnb.1063
Classification : 11N56,  14G42
Mots clés : Iwasawa theory, Iwasawa module, Galois module structure
@article{JTNB_2018__30_3_1017_0,
     author = {Mahiro Atsuta},
     title = {Finite $\Lambda $-submodules of {Iwasawa} modules for a {CM-field} for $p=2$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {1017--1035},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {30},
     number = {3},
     year = {2018},
     doi = {10.5802/jtnb.1063},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1063/}
}
Mahiro Atsuta. Finite $\Lambda $-submodules of Iwasawa modules for a CM-field for $p=2$. Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 1017-1035. doi : 10.5802/jtnb.1063. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1063/

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