Selmer groups for elliptic curves in l d -extensions of function fields of characteristic p
Annales de l'Institut Fourier, Volume 59 (2009) no. 6, p. 2301-2327

Let F be a function field of characteristic p>0, /F a l d -extension (for some prime lp) and E/F a non-isotrivial elliptic curve. We study the behaviour of the r-parts of the Selmer groups (r any prime) in the subextensions of via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of /F.

Soit F un corps de fonctions de caractéristique p>0, /F une l d -extension (pour un nombre premier lp) et E/F une courbe elliptique non-isotrivale. Nous étudions le comportement des r-parties des groupes de Selmer pour les sous-extensions de par des variantes du Théorème de contrôle de Mazur. Conséquemment, nous démontrons que la limite des groupes de Selmer est un module finiment co-engendré (parfois de cotorsion) sur l’algèbre d’Iwasawa de /F.

DOI : https://doi.org/10.5802/aif.2491
Classification:  11G05,  11R23
Keywords: Selmer groups, elliptic curves, function fields, Iwasawa theory
@article{AIF_2009__59_6_2301_0,
     author = {Bandini, Andrea and Longhi, Ignazio},
     title = {Selmer groups for elliptic curves in $\mathbb{Z}\_l^d$-extensions of function fields of characteristic $p$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {6},
     year = {2009},
     pages = {2301-2327},
     doi = {10.5802/aif.2491},
     zbl = {1207.11061},
     mrnumber = {2640921},
     zbl = {pre05673897},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_6_2301_0}
}
Bandini, Andrea; Longhi, Ignazio. Selmer groups for elliptic curves in $\mathbb{Z}_l^d$-extensions of function fields of characteristic $p$. Annales de l'Institut Fourier, Volume 59 (2009) no. 6, pp. 2301-2327. doi : 10.5802/aif.2491. http://www.numdam.org/item/AIF_2009__59_6_2301_0/

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