Breuil-Mézard conjectures for central division algebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2018
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908455005061120 |
|---|---|
| author | Dotto, Andrea |
| author_facet | Dotto, Andrea |
| contents | We formulate an analogue of the Breuil-Mézard conjecture for the group of units of a central division algebra over a $p$-adic local field, and we prove that it follows from the conjecture for $\mathrm{GL}_n$. To do so we construct a transfer of inertial types and Serre weights between the maximal compact subgroups of these two groups, in terms of Deligne-Lusztig theory, and we prove its compatibility with mod $p$ reduction, via the inertial Jacquet-Langlands correspondence and certain explicit character formulas. We also prove analogous statements for $\ell$-adic coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_06851 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Breuil-Mézard conjectures for central division algebras Dotto, Andrea Number Theory Representation Theory We formulate an analogue of the Breuil-Mézard conjecture for the group of units of a central division algebra over a $p$-adic local field, and we prove that it follows from the conjecture for $\mathrm{GL}_n$. To do so we construct a transfer of inertial types and Serre weights between the maximal compact subgroups of these two groups, in terms of Deligne-Lusztig theory, and we prove its compatibility with mod $p$ reduction, via the inertial Jacquet-Langlands correspondence and certain explicit character formulas. We also prove analogous statements for $\ell$-adic coefficients. |
| title | Breuil-Mézard conjectures for central division algebras |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/1808.06851 |