The Atiyah class on algebraic stacks
Nikolas Kuhn

TL;DR
This paper extends the concept of the Atiyah class to algebraic stacks, providing a global obstruction theory for moduli stacks of complexes without relying on derived algebraic geometry.
Contribution
It generalizes Illusie's Atiyah class to complexes on algebraic stacks, establishing new properties and compatibilities useful for algebraic geometry.
Findings
Defines Atiyah class on algebraic stacks
Provides a global obstruction theory for moduli stacks
Establishes compatibilities with tensor products and determinants
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis
