Let be a function field of characteristic , a -extension (for some prime ) and a non-isotrivial elliptic curve. We study the behaviour of the -parts of the Selmer groups ( 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 .
Soit un corps de fonctions de caractéristique , une -extension (pour un nombre premier ) et une courbe elliptique non-isotrivale. Nous étudions le comportement des -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 .
Keywords: Selmer groups, elliptic curves, function fields, Iwasawa theory
Mot clés : groupes de Selmer, courbes elliptiques, corps de fonctions, théorie d’Iwasawa
Bandini, Andrea 1; Longhi, Ignazio 2
@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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.2491/} }
TY - JOUR AU - Bandini, Andrea AU - Longhi, Ignazio TI - Selmer groups for elliptic curves in $\mathbb{Z}_l^d$-extensions of function fields of characteristic $p$ JO - Annales de l'Institut Fourier PY - 2009 SP - 2301 EP - 2327 VL - 59 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2491/ DO - 10.5802/aif.2491 LA - en ID - AIF_2009__59_6_2301_0 ER -
%0 Journal Article %A Bandini, Andrea %A Longhi, Ignazio %T Selmer groups for elliptic curves in $\mathbb{Z}_l^d$-extensions of function fields of characteristic $p$ %J Annales de l'Institut Fourier %D 2009 %P 2301-2327 %V 59 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2491/ %R 10.5802/aif.2491 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2491/
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