The Atiyah class on algebraic stacks

Abstract

We generalize Illusie's definition of the Atiyah class to complexes with quasi-coherent cohomology on arbitrary algebraic stacks. We show that this gives a global obstruction theory for moduli stacks of complexes in algebraic geometry without derived methods. We give a similar generalization of the reduced Atiyah class, and show various useful properties for working with Atiyah classes, such as compatibilities between the reduced and ordinary Atiyah class, and compatibility with tensor products and determinants.

Originally part II of the author's PhD thesis. Slightly modified and generalized version. 52 pages

References in corpus (2)

• Enumerative invariants and wall-crossing formulae in abelian categories
• A blowup formula for virtual enumerative invariants on projective surfaces

Cited by in corpus (1)

• Simple obstructions and cone reduction