PreprintCC0arXiv
Maximal Unipotent Monodromy and p-adic Eigenvalue Formulas
Abstract
We establish p-adic formulas for the eigenvalues of Frobenius in the case of the family of hyperkloosterman sums. The deformation equation in this case has maximal unipotent monodromy, and the interplay of Frobenius and the differential equation plays an important role in establishing p-adic analytic formulas for the eigenvalues.
Related
- p-adic Hodge theory of unipotent completions revisited
- Harmonic Analysis on p-adic Unipotent Groups
- Uniform local models of quasi-unipotent p-adic differential equations
- A p-adic monodromy theorem for curves
- Characters and Polynomiality for Maximal Parabolic Unipotent Radicals in Finite Classical Groups
BibTeX
@misc{adolphson2026maximal,
title = {{Maximal Unipotent Monodromy and $p$-adic Eigenvalue Formulas}},
author = {Alan Adolphson and Steven Sperber and Hao Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05886},
eprint = {2611.05886},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05886},
note = {CC0},
}
RIS
TY - UNPB
TI - Maximal Unipotent Monodromy and p-adic Eigenvalue Formulas
AU - Alan Adolphson
AU - Steven Sperber
AU - Hao Zhang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05886
UR - https://arxiv.org/abs/2611.05886
AB - We establish p-adic formulas for the eigenvalues of Frobenius in the case of the family of hyperkloosterman sums. The deformation equation in this case has maximal unipotent monodromy, and the interplay of Frobenius and the differential equation plays an important role in establishing p-adic analytic formulas for the eigenvalues.
ER -