PreprintCC BY 4.0arXiv
A prismatic Riemann-Hilbert correspondence
Abstract
We study the category of constructible p-Kummer-étale sheaves on the log adic generic fiber (X,ℳD)η for the stratification induced by a horizontal normal crossings divisor D, showing that it is antiequivalent to a category of finitely generated unit Laurent crystals on the log prismatic site. We give a local description of finitely generated unit crystals on a framed log affine in terms of (φ,Γ)-modules, and show pushforward compatibility for strict log smooth proper morphisms.
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BibTeX
@misc{pentland2026prismatic,
title = {{A prismatic Riemann-Hilbert correspondence}},
author = {Dylan Pentland},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20466},
eprint = {2610.20466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20466},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A prismatic Riemann-Hilbert correspondence
AU - Dylan Pentland
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20466
UR - https://arxiv.org/abs/2610.20466
AB - We study the category of constructible p-Kummer-étale sheaves on the log adic generic fiber (X,ℳ_D)_η for the stratification induced by a horizontal normal crossings divisor D, showing that it is antiequivalent to a category of finitely generated unit Laurent crystals on the log prismatic site. We give a local description of finitely generated unit crystals on a framed log affine in terms of (φ,Γ)-modules, and show pushforward compatibility for strict log smooth proper morphisms.
ER -