Arithmetic McKay correspondence

2008/12/22 by Jian Zhou, Zhou, Jian
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.0812.4202

arxiv created 2008/12/22 · openalex publication_date 2008/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an arithmetic McKay correspondence which relates suitably defined zeta functions of some Deligne-Mumford stacks to the zeta functions of their crepant resolutions. Some examples are discussed.

Citations

• Crepant resolution conjecture in all genera for type A singularities
• Frobenius action on l-adic Chen-Ruan cohomology

Related

• Zeta Correspondences in Rank-n
• Hilbert schemes of points via McKay correspondences
• Zeta Functions on Arithmetic Surfaces
• A correspondence dual to McKay's
• On the Crepant Resolution Conjecture for Donaldson-Thomas Invariants