2022/09/16 by Adeel A. Khan, Khan, Adeel A., Charanya Ravi +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14F06 #14F42 #14L30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2209.07801
openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized cohomology theories like motivic cohomology and algebraic cobordism. We use this to prove a (higher) equivariant Grothendieck-Riemann-Roch theorem, comparing Borel-equivariant G-theory and equivariant Chow groups. We also give a Bernstein-Lunts-type gluing description of the infinity-category of equivariant sheaves on a scheme X, in terms of nonequivariant sheaves on X and sheaves on its Borel construction.