Extendability of differential forms via Cartier operators

Tatsuro Kawakami

Published 2022-07-28Version 1

Let $(X, B)$ be a pair of a normal variety over a perfect field of positive characteristic and a reduced divisor. We prove that if the Cartier isomorphism on the log smooth locus of $(X,B)$ extends to the whole $X$, then $(X,B)$ satisfies the logarithmic extension theorem. As applications, we show that the logarithmic (resp.~regular) extension theorem holds for a quotient singularity by a linearly reductive group scheme (resp.~a finite group scheme order prime to the characteristic). We also prove that the logarithmic extension theorem for one-forms for singularities of higher codimension holds under assumptions about Serre's condition.