Existence of moduli spaces for algebraic stacks

• 成果类型: Article
• 署名作者: Alper, Jarod; Halpern-Leistner, Daniel; Heinloth, Jochen
• 署名单位: University of Washington; University of Washington Seattle; Cornell University; University of Duisburg Essen
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01214-4
• 发表日期: 2023
• 页码: 949-1038
• 关键词: valuative criteria; tannaka duality; t-structures; bundles; STABILITY; families

摘要

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 T-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 G-bundles on curves and moduli spaces for objects in abelian categories.