A criterion for $p$-closedness of derivations in dimension two

Kentaro Mitsui; Nobuo Sato

A criterion for $p$-closedness of derivations in dimension two

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arxiv 2409.03442 v1 pith:IXOVJKQ3 submitted 2024-09-05 math.AG

Kentaro Mitsui , Nobuo Sato This is my paper · ORCID

classification math.AG

keywords criterionderivationsdimensiongaloistheoryarticlecertaincharacteristic

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Jacobson developed a counterpart of Galois theory for purely inseparable field extensions in positive characteristic. In his theory, a certain type of derivations replace the role of the generators of Galois groups. This article provides a convenient criterion for determining such derivations in dimension two. We also present examples demonstrating the efficiency of our criterion.

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Pathological MMP singularities as $\alpha_p$-quotients
math.AG 2025-01 conditional novelty 8.0 of 10

For every positive characteristic, the author constructs non-S3 terminal singularities of dimension p+1 and stable families with klt, Cohen-Macaulay, F-injective general fibers but non-S2 special fibers.

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