PreprintarXiv licencearXiv
Completed cohomology of Hilbert modular varieties below middle degree
Abstract
We study the locally analytic vectors of completed cohomology of Hilbert modular varieties below middle degree. Our main result says that the universal enveloping algebra action has to factor through certain quotients. Application includes bounds on the Gelfand-Kirillov dimension and a density result. The method is a continuation of our joint work with Kai-Wen Lan.
Related
- Plectic Lie Algebra Action on Hilbert modular varieties
- Sparsity of rational points on torsion level covers of Hilbert modular varieties
- Hochschild cohomology of Hilbert schemes of points on surfaces
- Igusa stacks and the cohomology of Shimura varieties
- Cohomology of integral structure sheaves for open varieties
BibTeX
@misc{pan2026completed,
title = {{Completed cohomology of Hilbert modular varieties below middle degree}},
author = {Lue Pan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27310},
eprint = {2609.27310},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27310},
}
RIS
TY - UNPB
TI - Completed cohomology of Hilbert modular varieties below middle degree
AU - Lue Pan
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27310
UR - https://arxiv.org/abs/2609.27310
AB - We study the locally analytic vectors of completed cohomology of Hilbert modular varieties below middle degree. Our main result says that the universal enveloping algebra action has to factor through certain quotients. Application includes bounds on the Gelfand-Kirillov dimension and a density result. The method is a continuation of our joint work with Kai-Wen Lan.
ER -