Extending one-forms on $F$-regular singularities

Abstract

We prove the logarithmic extension theorem for one-forms on strongly $F$-regular singularities. Additionally, we establish the logarithmic extension theorem for one-forms on three-dimensional klt singularities in characteristic $p>41$. 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.

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