A Proof of the Integral Identity via Braden's Theorem

2024/10/15 by Florian Ivorra, Ivorra, Florian
Computer Science · #14C15 #14F42 #32S30 #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2410.11365

openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to provide a very short proof of a generalized categorified version, within the motivic stable homotopy category of Morel and Voevodsky, of the integral identity for virtual motives conjectured by Kontsevich and Soibelman. Our proof is an application of an important result in geometric representation theory due to Braden and known as the hyperbolic localization/restriction theorem. Though originally proved in the context of etale sheaves (or sheaves on the associated complex analytic space in the case of complex algebraic varieties) Braden's theorem turns out to hold also in the context of motivic sheaves, at least in the special case of vector bundles with a linear G_m-action.

Related

• The integral identity conjecture in motivic homotopy theory
• On a theorem of Braden
• Integral Motivic Sheaves And Geometric Representation Theory
• Motivic integration on special rigid varieties and the motivic integral identity conjecture
• Integration of Voevodsky motives