PreprintarXiv licencearXiv
Log blow-ups and global resolutions in rigid geometry
Abstract
In this article, we study log blow-ups in the setting of log adic spaces. As in the theory of log schemes, we prove the existence of global resolutions of toric singularities for fs log adic spaces log smooth over a p-adic field, and the acyclicity of certain sheaves under log blow-ups. One new feature of (log) rigid analytic varieties is their integral structure sheaf: we prove that it is also almost acyclic under log blow-ups in the Kummer étale topology. We also supply some foundational results on log adic spaces.
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BibTeX
@misc{shao2026blowups,
title = {{Log blow-ups and global resolutions in rigid geometry}},
author = {Xinyu Shao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31265},
eprint = {2610.31265},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31265},
}
RIS
TY - UNPB
TI - Log blow-ups and global resolutions in rigid geometry
AU - Xinyu Shao
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31265
UR - https://arxiv.org/abs/2610.31265
AB - In this article, we study log blow-ups in the setting of log adic spaces. As in the theory of log schemes, we prove the existence of global resolutions of toric singularities for fs log adic spaces log smooth over a p-adic field, and the acyclicity of certain sheaves under log blow-ups. One new feature of (log) rigid analytic varieties is their integral structure sheaf: we prove that it is also almost acyclic under log blow-ups in the Kummer étale topology. We also supply some foundational results on log adic spaces.
ER -