Extending one-forms on $F$-regular singularities
Algebraic Geometry
2026-04-07 v3 Commutative Algebra
Abstract
We prove the logarithmic extension theorem for one-forms on strongly -regular singularities. Additionally, we establish the logarithmic extension theorem for one-forms on three-dimensional klt singularities in characteristic . To this end, we reduce the problem to the logarithmic extension theorem for two-dimensional klt singularities with imperfect residue fields using a technique based on Cartier operators.
Keywords
Cite
@article{arxiv.2502.17148,
title = {Extending one-forms on $F$-regular singularities},
author = {Tatsuro Kawakami and Kenta Sato},
journal= {arXiv preprint arXiv:2502.17148},
year = {2026}
}
Comments
42 pages, v3: improved Theorem 3.2. The previous version of this preprint has been split into two parts. This version forms the first part. The second part, which concerns the classification of two-dimensional $F$-singularities, will be uploaded to arXiv soon