Cohomological and categorical concentration

2023/08/03 by Adeel A. Khan, Khan, Adeel A., Charanya Ravi +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2308.01652

openalex publication_date 2023/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a torus action on a compact space X, a fundamental result of Borel and Atiyah-Segal asserts that the equivariant cohomology of X is concentrated in the fixed locus X^T, up to inverting enough Chern classes. We prove an analogue for algebraic varieties over an arbitrary field. In fact, we deduce this from a categorification at the level of equivariant derived categories and even equivariant stable motivic homotopy categories, which also gives concentration at the level of Voevodsky motives and for homotopy K-theory.

Cited by

• Stable map quotients (and orbifold log resolutions) of Richardson varieties

Related

• The geometric concentration theorem
• Generalized cohomology theories for algebraic stacks
• The stacky concentration theorem
• Equivariant K-theory and Resolution II: Non-Abelian actions
• The motivic cobordism for group actions