Fargues-Scholze parameters and torsion vanishing for special orthogonal and unitary groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918146775973888 |
|---|---|
| author | Peng, Hao |
| author_facet | Peng, Hao |
| contents | We show that when $p$ is an odd prime, $K$ is an unramified finite extension of $\mathbb Q_p$ and $G$ is a pure inner form of an unramified special orthogonal group or unitary group over $K$, the Fargues-Scholze local Langlands correspondence for $G$ agrees with the semi-simplification of classical local Langlands correspondence. As applications, we construct an unambiguous local Langlands correspondence for even orthogonal groups, deduce Fargues' eigen-sheaf conjecture, and prove new torsion vanishing results for orthogonal and unitary Shimura varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fargues-Scholze parameters and torsion vanishing for special orthogonal and unitary groups Peng, Hao Number Theory Algebraic Geometry Representation Theory 22E50, 11S37 We show that when $p$ is an odd prime, $K$ is an unramified finite extension of $\mathbb Q_p$ and $G$ is a pure inner form of an unramified special orthogonal group or unitary group over $K$, the Fargues-Scholze local Langlands correspondence for $G$ agrees with the semi-simplification of classical local Langlands correspondence. As applications, we construct an unambiguous local Langlands correspondence for even orthogonal groups, deduce Fargues' eigen-sheaf conjecture, and prove new torsion vanishing results for orthogonal and unitary Shimura varieties. |
| title | Fargues-Scholze parameters and torsion vanishing for special orthogonal and unitary groups |
| topic | Number Theory Algebraic Geometry Representation Theory 22E50, 11S37 |
| url | https://arxiv.org/abs/2503.04623 |