2022/06/27 by Eleonore Faber, Colin Ingalls, Faber, Eleonore +5
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2206.13359
openalex publication_date 2022/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Let k be an algebraically closed field of characteristic ≥ 7 or zero. Let A be a tame order of global dimension 2 over a normal surface X over k such that Z(A)=OX is locally a direct summand of A. We prove that there is a μN-gerbe X over a smooth tame algebraic stack whose generic stabilizer is trivial, with coarse space X such that the category of 1-twisted coherent sheaves on X is equivalent to the category of coherent sheaves of modules on A. Moreover, the stack X is constructed explicitly through a sequence of root stacks, canonical stacks, and gerbes. This extends results of Reiten and Van den Bergh to finite characteristic and the global situation. As applications, in characteristic 0 we prove that such orders are geometric noncommutative schemes in the sense of Orlov, and we study relations with Hochschild cohomology and Connes' convolution algebra.