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Pure and Applied Mathematics Quarterly
Volume 19 (2023)
On the $\mu$ equals zero conjecture for fine Selmer groups in Iwasawa theory
Pages: 641 – 680
We study the Iwasawa theory of the fine Selmer groups associated to Galois representations arising from modular forms. The vanishing of the $\mu$-invariant is shown to follow in some cases from a natural property satisfied by Galois deformation rings. We outline conditions under which the $\mu = 0$ conjecture is shown to hold for various Galois representations of interest.
Iwasawa $\mu$-invariant, fine Selmer groups, adjoint representations, deformations of Galois representations
2010 Mathematics Subject Classification
Primary 11R23. Secondary 11F11, 11F80, 11G05.
The first-named author was supported by the CRM-Simons bridge postdoctoral fellowship.
The third-named author gratefully acknowledges support from NSERC Discovery grant 2019-03987
Received 3 October 2022
Received revised 8 December 2022
Accepted 11 January 2023
Published 7 April 2023