Extending one-forms on $F$-regular singularities

TL;DR

This paper proves the logarithmic extension theorem for one-forms on strongly F-regular singularities and three-dimensional klt singularities in characteristic p>41, using reduction techniques involving Cartier operators.

Contribution

It extends the logarithmic extension theorem to new classes of singularities in positive characteristic, including three-dimensional klt singularities.

Findings

Proves the extension theorem for strongly F-regular singularities.

Establishes the theorem for three-dimensional klt singularities in characteristic p>41.

Reduces the problem to two-dimensional cases with imperfect residue fields.

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.