Selmer groups for elliptic curves in l d -extensions of function fields of characteristic p
[Groupes de Selmer pour les courbes elliptiques en l d -extensions de corps de fonctions de caractéristique p]
Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2301-2327.

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.

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.

DOI : https://doi.org/10.5802/aif.2491
Classification : 11G05,  11R23
Mots clés : groupes de Selmer, courbes elliptiques, corps de fonctions, théorie d’Iwasawa
@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},
     pages = {2301--2327},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {59},
     number = {6},
     year = {2009},
     doi = {10.5802/aif.2491},
     zbl = {1207.11061},
     mrnumber = {2640921},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2491/}
}
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, Tome 59 (2009) no. 6, pp. 2301-2327. doi : 10.5802/aif.2491. http://www.numdam.org/articles/10.5802/aif.2491/

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