Existence of moduli spaces for algebraic stacks

Jarod Alper; Daniel Halpern-Leistner; Jochen Heinloth

doi:10.1007/s00222-023-01214-4

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arXiv · 1812.01128

Existence of moduli spaces for algebraic stacks

Jarod Alper·Daniel Halpern-Leistner·Jochen Heinloth

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Abstract

We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a generalization of the Keel--Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to construct proper moduli spaces parameterizing semistable $\mathcal{G}$-bundles on curves and moduli spaces for objects in abelian categories.

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Jarod Alper, Daniel Halpern-Leistner, Jochen Heinloth. 2018-12-03. Existence of moduli spaces for algebraic stacks. https://doi.org/10.1007/s00222-023-01214-4

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