Extending one-forms on F-regular singularities
Extending one-forms on F-regular singularities
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Tatsuro Kawakami, Kyoto University
Fine Hall 110
For a normal variety X, we say that X satisfies the logarithmic extension theorem for i-forms if, for every proper birational morphism f : Y to X, every i-form on the regular locus of X extends to a logarithmic i-form on Y. This property fundamentally relates differential forms and singularities, and many results are known over the field of complex numbers.
In this talk, we discuss the extension theorem in positive characteristic. In particular, we prove the logarithmic extension theorem for one-forms on strongly F-regular singularities by utilizing Cartier operators.
Joint work with Kenta Sato.