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Fedder-type criterion for quasi-$F^e$-splitting and quasi-$F$-regularity

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arxiv 2505.09015 v4 pith:J3TKBG5I submitted 2025-05-13 math.AG math.AC

Shou Yoshikawa This is my paper · ORCID
classification math.AGmath.AC
keywords quasi-criteriaregularitysplitsplittingadjunctionapplicationcharacterize
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abstract

We study quasi-$F^e$-split and quasi-$F$-regular singularities, which generalize Yobuko's quasi-$F$-splitting. We establish Fedder type criteria that characterize these properties for hypersurfaces. These criteria offer explicit tools for computation and verification. As an application, we construct a counterexample to the inversion of adjunction for quasi-$F$-regularity and compute the quasi-$F$-split threshold of the cone over the ordinary cusp.

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