2025/05/18 by Francesco Sala, Sala, Francesco, Laurent Schadeck +3 · 2 citations
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.2505.12357
openalex publication_date 2025/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a quotient of a regular noetherian separated algebraic space X over a field by an affine algebraic group G having finite stabilizers (with some mild technical conditions), G. Vezzosi and A. Vistoli defined the geometric part of the rational equivariant K-theory K(X,G) and conjectured that it is isomorphic to the rational K-theory of the quotient X/G. In this paper we refine the construction of geometric K-theory to the rational K-theory of a quotient stack [X/G] over an arbitrary excellent base; we show that it is part of an intrinsic decomposition of the K-theory of the stack and prove many properties that make it amenable to computations.