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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/2502.15560 |
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| _version_ | 1866911406397325312 |
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| author | Forrás, Ben |
| author_facet | Forrás, Ben |
| contents | We study graduated orders over completed group rings of $1$-dimensional admissible $p$-adic Lie groups, and verify the equivariant $p$-adic Artin conjecture for such orders. Following Jacobinski and Plesken, we obtain a formula for the conductor of a graduated order into a self-dual order. We also refine Nickel's central conductor formula by determining a hitherto implicit exponent $r_χ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graduated orders over completed group rings and conductor formulæ Forrás, Ben Rings and Algebras Number Theory 16H10 (Primary), 16H20, 11R23 (Secondary) We study graduated orders over completed group rings of $1$-dimensional admissible $p$-adic Lie groups, and verify the equivariant $p$-adic Artin conjecture for such orders. Following Jacobinski and Plesken, we obtain a formula for the conductor of a graduated order into a self-dual order. We also refine Nickel's central conductor formula by determining a hitherto implicit exponent $r_χ$. |
| title | Graduated orders over completed group rings and conductor formulæ |
| topic | Rings and Algebras Number Theory 16H10 (Primary), 16H20, 11R23 (Secondary) |
| url | https://arxiv.org/abs/2502.15560 |