Effectivity of Brauer-Manin obstructions on surfaces

Andrew Kresch; Yuri Tschinkel

doi:10.1016/j.aim.2010.11.012

Effectivity of Brauer-Manin obstructions on surfaces

Andrew Kresch, Yuri Tschinkel

Mathematics

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

Abstract

We study Brauer-Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.

Original language	English (US)
Pages (from-to)	4131-4144
Number of pages	14
Journal	Advances in Mathematics
Volume	226
Issue number	5
DOIs	https://doi.org/10.1016/j.aim.2010.11.012
State	Published - Mar 20 2011

Keywords

Azumaya algebras
Brauer-Manin obstruction
Effectivity
Primary
Secondary

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2010.11.012

Cite this

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title = "Effectivity of Brauer-Manin obstructions on surfaces",

abstract = "We study Brauer-Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.",

keywords = "Azumaya algebras, Brauer-Manin obstruction, Effectivity, Primary, Secondary",

author = "Andrew Kresch and Yuri Tschinkel",

note = "Funding Information: The first author was supported by the SNF. The second author was supported by NSF grants 0739380 and 0901777. Both authors acknowledge the gracious support of the Forschungsinstitut f{\"u}r Mathematik of the ETH, which hosted the second author for a research visit in Zurich.",

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AU - Tschinkel, Yuri

N1 - Funding Information: The first author was supported by the SNF. The second author was supported by NSF grants 0739380 and 0901777. Both authors acknowledge the gracious support of the Forschungsinstitut für Mathematik of the ETH, which hosted the second author for a research visit in Zurich.

PY - 2011/3/20

Y1 - 2011/3/20

N2 - We study Brauer-Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.

AB - We study Brauer-Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.

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KW - Brauer-Manin obstruction

KW - Effectivity

KW - Primary

KW - Secondary

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ER -

Effectivity of Brauer-Manin obstructions on surfaces

Abstract

Keywords

ASJC Scopus subject areas

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