On the $μ$-invariants of residually reducible Galois representations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915037689413632 |
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| author | Ray, Anwesh Sujatha, R. |
| author_facet | Ray, Anwesh Sujatha, R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_10797 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the $μ$-invariants of residually reducible Galois representations Ray, Anwesh Sujatha, R. Number Theory 11F80, 11R23, 11G05, 11R34 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. |
| title | On the $μ$-invariants of residually reducible Galois representations |
| topic | Number Theory 11F80, 11R23, 11G05, 11R34 |
| url | https://arxiv.org/abs/2104.10797 |