On the corank of the fine Selmer group of an elliptic curve over a ℤ_p-extension

2022/08/28 by Ray, Anwesh
#11G05 #11R23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2208.13247

Abstract

Let p be an odd prime and F_∞ be a ℤ_p-extension of a number field F. Given an elliptic curve E over F, we study the structure of the fine Selmer group over F_∞. It is shown that under certain conditions, the fine Selmer group is a cofinitely generated module over ℤ_p and furthermore, we obtain an upper bound for its corank (i.e., the λ-invariant), in terms of various local and global invariants.

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