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arXiv · 2104.10797

On the $μ$-invariants of residually reducible Galois representations

Anwesh Ray·R. Sujatha
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Abstract

The Iwasawa $μ$-invariant of the Selmer group of a residually reducible Galois representation arising from a Hecke eigencuspform is studied. Furthermore, certain Iwasawa-invariants refining the $μ$-invariant are defined and analyzed. As an application, we show that given any reducible mod-$p$ Galois representation $\barρ$ and any choice of integer $N\geq 1$, there is a modular Galois representation lifting $\barρ$ whose associated Selmer group has $μ$-invariant $\geq N$. This is a refinement of Serre's conjecture in the residually reducible case.

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Anwesh Ray, R. Sujatha. 2023-07-12. On the $μ$-invariants of residually reducible Galois representations. https://doi.org/10.1353/ajm.2024.a944359

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