[1306.2047] Notes on the fine Selmer groups
arxiv.org › abs › 1306Jun 09, 2013 · In this paper, we study the fine Selmer groups attached to a Galois module defined over a commutative complete Noetherian ring with finite residue field of characteristic p. Namely, we are interested in its properties upon taking residual representation and within field extensions. In particular, we will show that the variation of the fine Selmer group in a cyclotomic $\\Zp$-extension is ...
[1704.04893] Fine Selmer Groups and Isogeny Invariance
arxiv.org › abs › 1704Apr 17, 2017 · We investigate fine Selmer groups for elliptic curves and for Galois representations over a number field. More specifically, we discuss Conjecture A, which states that the fine Selmer group of an elliptic curve over the cyclotomic extension is a finitely generated $\\mathbb{Z}_p$-module. The relationship between this conjecture and Iwasawa's classical $μ=0$ conjecture is clarified. We also ...