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

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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 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.

Original languageEnglish (US)
Pages (from-to)655-705
Number of pages51
JournalAnnals of Mathematics
Volume195
Issue number2
DOIs
StatePublished - Mar 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Mixed characteristic
  • Pushouts
  • Quotients
  • Semi-ample
  • Universal homeomorphisms

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