Year: 2024
Type: article
Abstract: : The Iwasawa $\mu$-invariant of the Selmer group of a residually reducible Galois representation arising from a Hecke eigencuspform is studied. Furthermore, certain Iwasawa-invariants refining the $\mu$-invariant are defined and analyzed. As an application, we show that given a reducible mod-$p$ Galois representation $\bar{\rho}$ and any choice of integer $N\geq 1$, there is a modular Galois representation lifting $\bar{\rho}$ whose associated Selmer group has $\mu$-invariant $\geq N$. This is a refinement of Serre's conjecture in the residually reducible case.
Source: American Journal of Mathematics
Authors: Anwesh Ray, R. Sujatha
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404596876