On the Euler characteristic of $S$-arithmetic groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910025871523840 |
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| author | Kammeyer, Holger Serafini, Giada |
| author_facet | Kammeyer, Holger Serafini, Giada |
| contents | We show that the sign of the Euler characteristic of an $S$-arithmetic subgroup of a simple algebraic group depends on the $S$-congruence completion only, except possibly in type ${}^6 D_4$. Consequently, the sign is a profinite invariant for such $S$-arithmetic groups with the congruence subgroup property. This generalizes previous work of the first author with Kionke--Raimbault--Sauer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05050 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Euler characteristic of $S$-arithmetic groups Kammeyer, Holger Serafini, Giada Group Theory Number Theory 22E40, 20E18, 11E72 We show that the sign of the Euler characteristic of an $S$-arithmetic subgroup of a simple algebraic group depends on the $S$-congruence completion only, except possibly in type ${}^6 D_4$. Consequently, the sign is a profinite invariant for such $S$-arithmetic groups with the congruence subgroup property. This generalizes previous work of the first author with Kionke--Raimbault--Sauer. |
| title | On the Euler characteristic of $S$-arithmetic groups |
| topic | Group Theory Number Theory 22E40, 20E18, 11E72 |
| url | https://arxiv.org/abs/2405.05050 |