Work

Extendability of differential forms via Cartier operators

Year: 2024

Type: article

Abstract: Let X be a normal variety over a perfect field of positive characteristic and B a reduced divisor on X . We prove that if the Cartier isomorphism on the log smooth locus of (X,B) extends to the entire X , then (X,B) satisfies the logarithmic extension theorem for differential forms. As an application, we show that the logarithmic extension theorem holds for good quotients of smooth varieties by actions of reduced linearly reductive group schemes. In addition, the logarithmic extension theorem for one-forms holds for singularities of higher codimension under assumptions about Serre’s condition. We also prove that tame quotients satisfy the regular extension theorem.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1542

Author: Tatsuro Kawakami

Institution: Kyoto University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Awards: Study of singularities via Cartier operators, G7950615877