Control theorem and functional equation of Selmer groups over p-adic Lie extensions

Jha, Somnath; Ochiai, Tadashi

doi:10.1007/s00029-020-00607-0

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Algebraic Functional Equation1

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2021

2023

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Cited by 3 publications

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“…Since the theorem relates characteristic ideals of the dual Selmer groups, it is a necessary assumption that the dual Selmer groups are Λ-torsion. Proof of our algebraic functional equation follows an argument similar to arguments provided in [PR2,JP,JM,JO].…”

Section: Algebraic Functional Equationmentioning

confidence: 99%

On characteristic ideal of Selmer group associated to Artin representations

Majumdar¹,

Panda²

2022

Preprint

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Selmer group for an Artin representation over totally real fields was studied by Greenberg [Gr1,Gr4] and Vatsal [Va]. In this paper we study the Selmer groups for an Artin representation over a totally complex field. We establish an algebraic function of the characteristic ideal of the Selmer group associated to Artin representation over the cyclotomic Zpextension of the rational numbers under certain mild hypotheses and construct several examples to illustrate our result. We also prove that in this situation µ-invariant of the dual Selmer group is independent of the choice of the lattice.

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Section: Algebraic Functional Equationmentioning

confidence: 99%