#### Vol. 3, No. 6, 2009

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Compactified moduli of projective bundles

### Max Lieblich

Vol. 3 (2009), No. 6, 653–695
##### Abstract

We present a method for compactifying stacks of PGL${}_{n}$-torsors (Azumaya algebras) on algebraic spaces. In particular, when the ambient space is a smooth projective surface we use our methods to show that various moduli spaces are irreducible and carry natural virtual fundamental classes. We also prove a version of the Skolem–Noether theorem for certain algebra objects in the derived category, which allows us to give an explicit description of the boundary points in our compactified moduli problem.

##### Keywords
projective bundles, moduli of stable bundles, Skolem–Noether theorem, derived categories, rigidification
Primary: 14D20
Secondary: 14D15