Ultra-Kolyvagin systems and non-ordinary Selmer groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909910310060032 |
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| author | Loeffler, David Zerbes, Sarah Livia |
| author_facet | Loeffler, David Zerbes, Sarah Livia |
| contents | We develop a machine for bounding Selmer groups of Galois representations via Euler systems in "non-ordinary" settings, using Pottharst's definition of Selmer groups via Robba-ring $(φ, Γ)$-modules. Our approach relies on Sweeting's interpretation of Kolyvagin derivative classes via non-principal ultrafilters. We apply these results to prove new cases of the cyclotomic Iwasawa main conjecture for non-ordinary Rankin--Selberg convolutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08793 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ultra-Kolyvagin systems and non-ordinary Selmer groups Loeffler, David Zerbes, Sarah Livia Number Theory 11R23, 11S25 We develop a machine for bounding Selmer groups of Galois representations via Euler systems in "non-ordinary" settings, using Pottharst's definition of Selmer groups via Robba-ring $(φ, Γ)$-modules. Our approach relies on Sweeting's interpretation of Kolyvagin derivative classes via non-principal ultrafilters. We apply these results to prove new cases of the cyclotomic Iwasawa main conjecture for non-ordinary Rankin--Selberg convolutions. |
| title | Ultra-Kolyvagin systems and non-ordinary Selmer groups |
| topic | Number Theory 11R23, 11S25 |
| url | https://arxiv.org/abs/2511.08793 |