2019/05/02 by Daniel Bergh, Bergh, Daniel, David Rydh +1 · 2 citations
Mathematics · #14A20 #14E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1905.00872
openalex publication_date 2019/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth and tame stack with finite inertia. We prove that there is a functorial sequence of blow-ups with smooth centers after which the stabilizers of X become abelian. Using this result, we can extend the destackification results of the first author to any smooth tame stack. We give applications to resolution of tame quotient singularities, prime-to-l alterations of singularities and weak factorization of Deligne-Mumford stacks. We also extend the abelianization result to infinite stabilizers in characteristic zero, generalizing earlier work of Reichstein-Youssin.