NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC

Louis Esser

doi:10.1090/proc/16140

NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC

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

Mathematics(all)
Applied Mathematics

Keywords

Brauer groups
étale cohomology

Access to Document

10.1090/proc/16140

Cite this

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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 = "Funding Information: Received by the editors February 11, 2021, and, in revised form, January 10, 2022, May 2, 2022, and May 12, 2022. 2020 Mathematics Subject Classification. Primary 14F22. Key words and phrases. Brauer groups, {\'e}tale cohomology. The author was supported in part by National Science Foundation grant DMS-1701237. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",

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doi = "10.1090/proc/16140",

language = "English (US)",

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AU - Esser, Louis

N1 - Funding Information: Received by the editors February 11, 2021, and, in revised form, January 10, 2022, May 2, 2022, and May 12, 2022. 2020 Mathematics Subject Classification. Primary 14F22. Key words and phrases. Brauer groups, étale cohomology. The author was supported in part by National Science Foundation grant DMS-1701237. Publisher Copyright: © 2022 American Mathematical Society.

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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

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JF - Proceedings of the American Mathematical Society

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ER -

NON-TORSION BRAUER GROUPS IN POSITIVE CHARACTERISTIC

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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