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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00911 |
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| _version_ | 1866908548681695232 |
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| author | Arenas-Carmona, Luis |
| author_facet | Arenas-Carmona, Luis |
| contents | It has been known for some time that the orders in the four dimensional matrix algebra over a local field that can be written as a finite intersection of maximal orders are precisely those whose Gorenstein closure is Eichler. In this paper, a similar characterization is given for orders whose Gorenstein closure is a Bass order. A second characterization, this time for the Bass orders themselves, is given in terms of their branches, i.e., maximal subgraphs of the Bruhat-Tits tree whose vertices are orders containing them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two characterizations of Bass orders via branches Arenas-Carmona, Luis Number Theory 11S45 (Primary), 16H10, 16G30 (Secondary) It has been known for some time that the orders in the four dimensional matrix algebra over a local field that can be written as a finite intersection of maximal orders are precisely those whose Gorenstein closure is Eichler. In this paper, a similar characterization is given for orders whose Gorenstein closure is a Bass order. A second characterization, this time for the Bass orders themselves, is given in terms of their branches, i.e., maximal subgraphs of the Bruhat-Tits tree whose vertices are orders containing them. |
| title | Two characterizations of Bass orders via branches |
| topic | Number Theory 11S45 (Primary), 16H10, 16G30 (Secondary) |
| url | https://arxiv.org/abs/2503.00911 |