The stack of spherical Langlands parameters
Number Theory
2025-10-30 v2 Representation Theory
Abstract
For a reductive group over a nonarchimedean local field, we define the stack of spherical Langlands parameters, using the inertia-invariants of the Langlands dual group. This generalizes the stack of unramified Langlands parameters in case the group is unramified. We then use this stack to deduce the Eichler--Shimura congruence relations for Hodge type Shimura varieties, without restrictions on the ramification.
Cite
@article{arxiv.2409.09522,
title = {The stack of spherical Langlands parameters},
author = {Thibaud van den Hove},
journal= {arXiv preprint arXiv:2409.09522},
year = {2025}
}
Comments
16 pages. New version contains an appendix by Sean Cotner, which allows us to generalize Theorem 2.5 compared to the previous version. Comments welcome!