Let F be a function field of characteristic p>0, \mathcalF/F a \mathbbZ_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 \mathcalF 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 \mathcalF/F.
Selmer groups for elliptic curves in Z_l^d-extensions of function fields of characteristic p
A. Bandini;
2009-01-01
Abstract
Let F be a function field of characteristic p>0, \mathcalF/F a \mathbbZ_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 \mathcalF 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 \mathcalF/F.File in questo prodotto:
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