The Atiyah class on algebraic stacks
arXiv:2306.13934 · doi:10.1017/fms.2024.109
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.
arXiv commentOriginally part II of the author's PhD thesis. Slightly modified and generalized version. 52 pages
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