Congruence rigidity of algebraic groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911646222385152 |
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| author | Baumann, Adrian Kammeyer, Holger |
| author_facet | Baumann, Adrian Kammeyer, Holger |
| contents | We identify the simple algebraic groups over number fields that are, in a suitable sense, determined by their finite adele points. Assuming CSP and Grothendieck rigidity, our results essentially characterize higher rank arithmetic groups that are profinitely solitary: the profinite commensurability class determines the commensurability class among finitely generated residually finite groups. This generalizes previous work of the second author with R. Spitler from split groups to arbitrary groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Congruence rigidity of algebraic groups Baumann, Adrian Kammeyer, Holger Group Theory Number Theory 11E72, 20E18, 22E40 We identify the simple algebraic groups over number fields that are, in a suitable sense, determined by their finite adele points. Assuming CSP and Grothendieck rigidity, our results essentially characterize higher rank arithmetic groups that are profinitely solitary: the profinite commensurability class determines the commensurability class among finitely generated residually finite groups. This generalizes previous work of the second author with R. Spitler from split groups to arbitrary groups. |
| title | Congruence rigidity of algebraic groups |
| topic | Group Theory Number Theory 11E72, 20E18, 22E40 |
| url | https://arxiv.org/abs/2605.03107 |