Greenberg’s conjecture for -extensions
3-Selmer groups for curves
We explicitly perform some steps of a 3-descent algorithm for the curves , 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
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 -extensions of function fields of characteristic
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 .
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