Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01398 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915974236602368 |
|---|---|
| author | Lei, Antonio Müller, Katharina Vallières, Daniel |
| author_facet | Lei, Antonio Müller, Katharina Vallières, Daniel |
| contents | Let $p$ be an odd rational prime and consider the cyclotomic number field $K = \mathbb{Q}(ζ_{p})$ of conductor $p$. We construct a directed graph $Y$ on $p-1$ vertices for which the torsion part of the corresponding Bowen--Franks group is closely related to the minus part of the class group of $K$. In particular, both groups have the same cardinality up to an explicit power of $p$. Furthermore, they are both $\mathrm{Gal}(K/\mathbb{Q})$-modules, and we prove the equality of the cardinalities of their isotypic components after tensoring them with the valuation ring of an appropriate $\ell$-adic field for $\ell \nmid p-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01398 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bowen--Franks groups and minus class groups of cyclotomic number fields with prime conductor Lei, Antonio Müller, Katharina Vallières, Daniel Number Theory Combinatorics Let $p$ be an odd rational prime and consider the cyclotomic number field $K = \mathbb{Q}(ζ_{p})$ of conductor $p$. We construct a directed graph $Y$ on $p-1$ vertices for which the torsion part of the corresponding Bowen--Franks group is closely related to the minus part of the class group of $K$. In particular, both groups have the same cardinality up to an explicit power of $p$. Furthermore, they are both $\mathrm{Gal}(K/\mathbb{Q})$-modules, and we prove the equality of the cardinalities of their isotypic components after tensoring them with the valuation ring of an appropriate $\ell$-adic field for $\ell \nmid p-1$. |
| title | Bowen--Franks groups and minus class groups of cyclotomic number fields with prime conductor |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2605.01398 |