In algebraic geometry of positive characteristics, singularities defined by the Frobenius map, including the notion of Frobenius-splitting, have played a crucial role. Moreover, there are powerful criteria, so-called Fedder's criteria, to confirm such properties. On the other hand, motivated by the study of Calabi-Yau varieties, Yobuko introduced the notion of quasi-Frobenius-splitting and Frobenius-split heights, which generalize and quantify the notion of F-splitting, and proved that Frobenius-split heights coincide with Artin-Mazur heights for Calabi-Yau varieties.
In this talk, I will give a generalization of Fedder's criteria to quasi-Frobenius-splitting, and introduce examples and applications of such criteria. This talk is based on a joint paper with Tatsuro Kawakami and Shou Yoshikawa.

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