Cohomology of finite subgroups of the plane Cremona group
Abstract
An equivariant stable birational invariant of an action of a finite group on a smooth projective variety is the first cohomology group of the Picard module. Bogomolov-Prokhorov and Shinder computed this for actions of cyclic groups on rational surfaces, with maximal stabilizers, in terms of the geometry of the fixed point locus. Using the Brauer group of the quotient stack, we extend the computation to more general actions and relate it to the equivariant Burnside group formalism.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Homotopy and Cohomology in Algebraic Topology
Alkaloids: synthesis and pharmacology
Publication details
- Journal / source
- Algebraic Geometry and Physics
- Publisher
- International Press of Boston
- Volume
- 3
- Issue
- 1
- Pages
- 119–139
- Publication date
- 1 January 2026
- Language
- EN