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3-Selmer groups for curves y 2 = x 3 + a

Andrea Bandini — 2008

Czechoslovak Mathematical Journal

We explicitly perform some steps of a 3-descent algorithm for the curves y 2 = x 3 + a , a a nonzero integer. In general this will enable us to bound the order of the 3-Selmer group of such curves.

Stabilization in non-abelian Iwasawa theory

Andrea Bandini;  Fabio Caldarola — 2015

Acta Arithmetica

Let K/k be a ℤₚ-extension of a number field k, and denote by kₙ its layers. We prove some stabilization properties for the orders and the p-ranks of the higher Iwasawa modules arising from the lower central series of the Galois group of the maximal unramified pro-p-extension of K (resp. of the kₙ).

Selmer groups for elliptic curves in ℤ l d -extensions of function fields of characteristic p

Andrea Bandini;  Ignazio Longhi — 2009

Annales de l’institut Fourier

Let F be a function field of characteristic p > 0 , ℱ / F a ℤ l d -extension (for some prime l ≠ 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 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 ℱ / F .

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