NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC

Louis Esser

doi:10.1090/proc/16140

NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC

Louis Esser

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

Abstract

Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with non-torsion Brauer group. In contrast, we demonstrate that such examples cannot exist over the algebraic closure of a finite field.

Original language	English (US)
Pages (from-to)	527-531
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	2
DOIs	https://doi.org/10.1090/proc/16140
State	Published - Feb 1 2023
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Brauer groups
étale cohomology

Access to Document

10.1090/proc/16140

Cite this

@article{110a2292e447433481615cbe5b95ec07,

title = "NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC",

abstract = "Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with non-torsion Brauer group. In contrast, we demonstrate that such examples cannot exist over the algebraic closure of a finite field.",

keywords = "Brauer groups, {\'e}tale cohomology",

author = "Louis Esser",

note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",

year = "2023",

month = feb,

day = "1",

doi = "10.1090/proc/16140",

language = "English (US)",

volume = "151",

pages = "527--531",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "2",

}

TY - JOUR

T1 - NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC

AU - Esser, Louis

PY - 2023/2/1

Y1 - 2023/2/1

N2 - Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with non-torsion Brauer group. In contrast, we demonstrate that such examples cannot exist over the algebraic closure of a finite field.

AB - Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with non-torsion Brauer group. In contrast, we demonstrate that such examples cannot exist over the algebraic closure of a finite field.

KW - Brauer groups

KW - étale cohomology

UR - https://www.scopus.com/pages/publications/85144646272

UR - https://www.scopus.com/pages/publications/85144646272#tab=citedBy

U2 - 10.1090/proc/16140

DO - 10.1090/proc/16140

M3 - Article

AN - SCOPUS:85144646272

SN - 0002-9939

VL - 151

SP - 527

EP - 531

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this