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Existence of moduli spaces for algebraic stacks

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arxiv 1812.01128 v5 pith:LTDUXUWN submitted 2018-12-03 math.AG

Existence of moduli spaces for algebraic stacks

classification math.AG
keywords modulialgebraicspacesgoodobjectsproperresultssemistable
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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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Cited by 3 Pith papers

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