Geodesic
The Atiyah class on algebraic stacks
Forum of Mathematics, Sigma, Tome 12 (2024)

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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 we 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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     author = {Nikolas Kuhn},
     title = {The {Atiyah} class on algebraic stacks},
     journal = {Forum of Mathematics, Sigma},
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     doi = {10.1017/fms.2024.109},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.109/}
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Nikolas Kuhn. The Atiyah class on algebraic stacks. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.109

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