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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12899 |
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| _version_ | 1866917159349780480 |
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| author | Combes, Lewis |
| author_facet | Combes, Lewis |
| contents | We present methods to compute Selmer groups associated to mod p Galois representations rho over a number field K, with a particular focus on comparing their ranks with periods coming from cohomology classes associated to rho by Serre's conjecture. This provides evidence for a loose version of a "mod p Bloch-Kato conjecture", where the vanishing of a period is predicted to capture the presence of rank in a Selmer group. Our methods are explicit, and implemented in Magma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing Selmer groups associated to mod p Galois representations Combes, Lewis Number Theory 11R34, 11Y40 We present methods to compute Selmer groups associated to mod p Galois representations rho over a number field K, with a particular focus on comparing their ranks with periods coming from cohomology classes associated to rho by Serre's conjecture. This provides evidence for a loose version of a "mod p Bloch-Kato conjecture", where the vanishing of a period is predicted to capture the presence of rank in a Selmer group. Our methods are explicit, and implemented in Magma. |
| title | Computing Selmer groups associated to mod p Galois representations |
| topic | Number Theory 11R34, 11Y40 |
| url | https://arxiv.org/abs/2512.12899 |