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

Pages 655-705 from Volume 195 (2022), Issue 2 by Jakub Witaszek

Abstract

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 Kollár’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.

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Keywords
, , , ,
Mathematical Subject Classification
Primary: , , ,
DOI
https://doi.org/10.4007/annals.2022.195.2.4
MR
4387235
zbMATH
7483864
Milestones
Received: 11 March 2020
Revised: 9 July 2021
Accepted: 1 October 2021
Published online: 28 February 2022

Authors

Jakub Witaszek

University of Michigan
Ann Arbor, MI