2019/01/30 by Alexander Vitanov, Vitanov, Alexander
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1901.11077
openalex publication_date 2019/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we realize the sheaf of Cherednik algebras H1, c, X, G on a general good complex orbifold X/G, originally introduced by Etingof for smooth complex varieties with an action by a finite group, by gluing sheaves of flat sections of flat holomorphic vector bundles on orbit type strata in X which result from a localization procedure. In the case, when c is formal, this construction can be interpreted as a formal deformation of DX\rtimes\mathbb CG via Gel'fand-Kazhdan formal geometry. Contrary to the original definition of H1, c, X, G the presented construction permits the computation of trace densities, Hochschild homologies and an algebraic index theorem for formal deformations of DX\rtimes\mathbb CG. We also hope that the methods developed here will contribute towards a full proof of Dolgushev-Etingof's conjecture.