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

Jakub Witaszek

doi:10.4007/annals.2022.195.2.4

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

Jakub Witaszek

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 language	English (US)
Pages (from-to)	655-705
Number of pages	51
Journal	Annals of Mathematics
Volume	195
Issue number	2
DOIs	https://doi.org/10.4007/annals.2022.195.2.4
State	Published - Mar 2022
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Mixed characteristic
Pushouts
Quotients
Semi-ample
Universal homeomorphisms

Access to Document

10.4007/annals.2022.195.2.4

Cite this

@article{3381a368dda046aaa2c743bee072817b,

title = "Keel's base point free theorem and quotients in mixed characteristic",

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.",

keywords = "Mixed characteristic, Pushouts, Quotients, Semi-ample, Universal homeomorphisms",

author = "Jakub Witaszek",

note = "Publisher Copyright: {\textcopyright} 2022. Department of Mathematics, Princeton University.",

year = "2022",

month = mar,

doi = "10.4007/annals.2022.195.2.4",

language = "English (US)",

volume = "195",

pages = "655--705",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

number = "2",

}

TY - JOUR

T1 - Keel's base point free theorem and quotients in mixed characteristic

AU - Witaszek, Jakub

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

KW - Mixed characteristic

KW - Pushouts

KW - Quotients

KW - Semi-ample

KW - Universal homeomorphisms

UR - http://www.scopus.com/inward/record.url?scp=85131953083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85131953083&partnerID=8YFLogxK

U2 - 10.4007/annals.2022.195.2.4

DO - 10.4007/annals.2022.195.2.4

M3 - Article

AN - SCOPUS:85131953083

SN - 0003-486X

VL - 195

SP - 655

EP - 705

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this