Let F be a function field of characteristic p>0, \mathcal{F}/F a \mathbb{Z}_l^d-extension (for some prime l\neq p) 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 \mathcal{F} 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 \mathcal{F}/F.

Selmer groups for elliptic curves in Z_l^d-extensions of function fields of characteristic p / Bandini, Andrea; I., Longhi. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 1777-5310. - 59:(2009), pp. 2301-2327. [10.5802/aif.2491]

Selmer groups for elliptic curves in Z_l^d-extensions of function fields of characteristic p

BANDINI, Andrea;
2009-01-01

Abstract

Let F be a function field of characteristic p>0, \mathcal{F}/F a \mathbb{Z}_l^d-extension (for some prime l\neq p) 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 \mathcal{F} 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 \mathcal{F}/F.
2009
Selmer groups for elliptic curves in Z_l^d-extensions of function fields of characteristic p / Bandini, Andrea; I., Longhi. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 1777-5310. - 59:(2009), pp. 2301-2327. [10.5802/aif.2491]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2358880
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