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Potential semistability of Finite height Galois representations: Relative case
Abstract
Let K be a p-adic field. We define the notion of finite height for an étale ℤp-local system on a smooth affinoid adic space 𝒳 over K with semistable reduction. Using analytic prismatic F-crystals and purity results of Du-Liu-Moon-Shimizu (arXiv:2404.19603), we prove that if an étale ℤp-local system over 𝒳 is of finite height then its pullback along a finite étale cover of 𝒳 is semistable. This answers a question of Tong Liu in the relative setting.
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BibTeX
@misc{mondal2026potential,
title = {{Potential semistability of Finite height Galois representations: Relative case}},
author = {Kaustabh Mondal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.26043},
eprint = {2606.26043},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26043},
}
RIS
TY - UNPB
TI - Potential semistability of Finite height Galois representations: Relative case
AU - Kaustabh Mondal
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2606.26043
UR - https://arxiv.org/abs/2606.26043
AB - Let K be a p-adic field. We define the notion of finite height for an étale ℤ_p-local system on a smooth affinoid adic space 𝒳 over K with semistable reduction. Using analytic prismatic F-crystals and purity results of Du-Liu-Moon-Shimizu (arXiv:2404.19603), we prove that if an étale ℤ_p-local system over 𝒳 is of finite height then its pullback along a finite étale cover of 𝒳 is semistable. This answers a question of Tong Liu in the relative setting.
ER -