Automorphic congruences between torsion cohomological classes
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909819048296448 |
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| author | Pascal, Boyer |
| author_facet | Pascal, Boyer |
| contents | For two representations of some local division algebra, congruent modulo $l$, giving rise to two Harris-Taylor local systems on the corresponding Newton strata of the special fiber of a KHT Shimura varieties, we prove that the $l$-torsion of each of their cohomology groups with compact supports are isomorphic, or equivalently the free quotients of each of the cohomology groups are congruent modulo $l$. We then deduce the construction of accurate non tempered automorphic congruences for a similitude group $G/\mathbb Q$ with signature $(1,d-1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_06048 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Automorphic congruences between torsion cohomological classes Pascal, Boyer Number Theory For two representations of some local division algebra, congruent modulo $l$, giving rise to two Harris-Taylor local systems on the corresponding Newton strata of the special fiber of a KHT Shimura varieties, we prove that the $l$-torsion of each of their cohomology groups with compact supports are isomorphic, or equivalently the free quotients of each of the cohomology groups are congruent modulo $l$. We then deduce the construction of accurate non tempered automorphic congruences for a similitude group $G/\mathbb Q$ with signature $(1,d-1)$. |
| title | Automorphic congruences between torsion cohomological classes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2201.06048 |