# Existence of moduli spaces for algebraic stacks.

@article{Alper2018ExistenceOM, title={Existence of moduli spaces for algebraic stacks.}, author={Jarod Alper and Daniel Halpern-Leistner and Jochen Heinloth}, journal={arXiv: Algebraic Geometry}, year={2018} }

We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space. This theorem provides a generalization of the Keel--Mori theorem to moduli problems whose objects have positive dimensional automorphism groups. We also prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. Using these results we find conditions for the good moduli space to be separated or proper. To illustrate our method, we apply these…

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