PreprintCC BY 4.0arXiv
Reduction modulo p of crystalline Galois representations via μ_p-equivariance
Abstract
For a crystalline representation of the absolute Galois group of Q_p, with given Hodge-Tate weights, we obtain new constraints on the inertial weights of its mod p reduction. This allows us to formulate an explicit Serre weight conjecture, in the generality of L-parameters for unramified connected reductive groups over Q_p, and to prove the elimination direction of this conjecture. The proof uses prismatic techniques to show that the reductions modulo p of the Breuil-Kisin modules attached to crystalline Galois representations acquire a natural μ_p-equivariant structure. Combining this with results on the geometry of the μ_p-fixed points of affine Grassmannians leads to our new constraint.
Related
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BibTeX
@misc{bhatt2026reduction,
title = {{Reduction modulo p of crystalline Galois representations via μ_p-equivariance}},
author = {Bhargav Bhatt and Toby Gee and Mark Kisin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.08660},
eprint = {2607.08660},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.08660},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reduction modulo p of crystalline Galois representations via μ_p-equivariance
AU - Bhargav Bhatt
AU - Toby Gee
AU - Mark Kisin
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2607.08660
UR - https://arxiv.org/abs/2607.08660
AB - For a crystalline representation of the absolute Galois group of Q_p, with given Hodge-Tate weights, we obtain new constraints on the inertial weights of its mod p reduction. This allows us to formulate an explicit Serre weight conjecture, in the generality of L-parameters for unramified connected reductive groups over Q_p, and to prove the elimination direction of this conjecture. The proof uses prismatic techniques to show that the reductions modulo p of the Breuil-Kisin modules attached to crystalline Galois representations acquire a natural μ_p-equivariant structure. Combining this with results on the geometry of the μ_p-fixed points of affine Grassmannians leads to our new constraint.
ER -