2024/06/13 by Dhyan Aranha, Adeel A. Khan, Aranha, Dhyan +7
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2407.08747
openalex publication_date 2024/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a sufficient criterion for the Chow or algebraic bordism groups of an algebraic stack, localized at a set of Chern classes of line bundles, to be concentrated in some closed substack. This is a vast generalization of the torus fixed-point localization theorem in equivariant intersection theory, which is the special case of the stack quotient of a scheme X by an action of a torus T. Taking on the one hand an algebraic stack in place of X, we deduce a generalization of torus localization to algebraic stacks. Taking on the other hand any algebraic group G instead of T, we obtain a localization theorem in G-equivariant intersection theory.