Keel's base point free theorem and quotients in mixed characteristic

• 成果类型: Article
• 署名作者: Witaszek, Jakub
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.195.2.4
• 发表日期: 2022
• 页码: 655-705
• 关键词: minimal model program; geometric reductivity; conjecture; divisors; locus

摘要

We develop techniques of mimicking the Frobenius action in the study of universal homeomorphisms in mixed characteristic. As a consequence, we show a mixed characteristic Keel's base point free theorem obtaining applications towards the mixed characteristic Minimal Model Program, we generalise Kollar's theorem on the existence of quotients by finite equivalence relations to mixed characteristic, and we provide a new proof of the existence of quotients by affine group schemes.