Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fields
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909014372122624 |
|---|---|
| author | Ivančić, Jelena McDonald, Vaughan |
| author_facet | Ivančić, Jelena McDonald, Vaughan |
| contents | Let $p$ be a prime, and let $F$ be a CM field containing an imaginary quadratic field in which $p$ splits. We show that the locally analytic vectors of Hecke eigenspaces in the ($p$-adic) completed cohomology of $\mathrm{GL}_n/F$, localized at a non-Eisenstein decomposed generic maximal ideal, admit infinitesimal characters determined by the Sen operators of the corresponding Galois representations, thus confirming a conjecture of Dospinescu-Paškūnas-Schraen in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03519 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fields Ivančić, Jelena McDonald, Vaughan Number Theory Algebraic Geometry Let $p$ be a prime, and let $F$ be a CM field containing an imaginary quadratic field in which $p$ splits. We show that the locally analytic vectors of Hecke eigenspaces in the ($p$-adic) completed cohomology of $\mathrm{GL}_n/F$, localized at a non-Eisenstein decomposed generic maximal ideal, admit infinitesimal characters determined by the Sen operators of the corresponding Galois representations, thus confirming a conjecture of Dospinescu-Paškūnas-Schraen in this case. |
| title | Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fields |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2605.03519 |