An Explicit Derived Equivalence of Azumaya Algebras on K3 Surfaces via Koszul Duality

2011/04/21 by Colin Ingalls, Ingalls, Colin, Madeeha Khalid +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1104.4333

openalex publication_date 2011/04/21 · arxiv created 2014/01/07 · arxiv updated 2014/01/08 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider moduli spaces of Azumaya algebras on K3 surfaces and construct an example. In some cases we show a derived equivalence which corresponds to a derived equivalence between twisted sheaves. We prove if A and A' are Morita equivalent Azumaya algebras of degree r then 2r divides c₂(A) - c₂(A'). In particular this implies that if A is an Azumaya algebra on a K3 surface and c₂(A) is within 2r of its minimal bound then the moduli stack of Azumaya algebras with the same underlying gerbe, if non empty, is a proper algebraic space.

Related

• Blt Azumaya algebras and moduli of maximal orders
• Azumaya geometry and representation stacks
• Moduli Spaces of Sheaves on K3 Surfaces and Symplectic Stacks
• Non-Fine Moduli Spaces of Sheaves on K3 Surfaces
• Rational points in coarse moduli spaces and twisted representations