On the Brauer-Manin obstruction for degree-four del Pezzo surfaces

Jörg Jahnel; Damaris Schindler

doi:10.4064/aa8123-8-2016

On the Brauer-Manin obstruction for degree-four del Pezzo surfaces

Jörg Jahnel
, Damaris Schindler

University of Siegen

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

Abstract

We show that for every integer 1≤d≤4 and every finite set S of places, there exists a degree-d del Pezzo surface X over Q such that Br(X)/Br(Q)≅Z/2Z and the nontrivial Brauer class has a nonconstant local evaluation exactly at the places in S. For d=4, we prove that in all cases except S={∞}, this surface may be chosen diagonalisably over Q.

Original language	English
Pages (from-to)	301-319
Number of pages	19
Journal	Acta Arithmetica
Volume	176
Issue number	4
DOIs	https://doi.org/10.4064/aa8123-8-2016
Publication status	Published - 2016

Keywords

Brauer-Manin obstruction
Degree-4 del Pezzo surface

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BrauerFinal published version, 349 KBLicence: Taverne

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title = "On the Brauer-Manin obstruction for degree-four del Pezzo surfaces",

abstract = "We show that for every integer 1≤d≤4 and every finite set S of places, there exists a degree-d del Pezzo surface X over Q such that Br(X)/Br(Q)≅Z/2Z and the nontrivial Brauer class has a nonconstant local evaluation exactly at the places in S. For d=4, we prove that in all cases except S=\{∞\}, this surface may be chosen diagonalisably over Q.",

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AB - We show that for every integer 1≤d≤4 and every finite set S of places, there exists a degree-d del Pezzo surface X over Q such that Br(X)/Br(Q)≅Z/2Z and the nontrivial Brauer class has a nonconstant local evaluation exactly at the places in S. For d=4, we prove that in all cases except S={∞}, this surface may be chosen diagonalisably over Q.

KW - Brauer-Manin obstruction

KW - Degree-4 del Pezzo surface

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DO - 10.4064/aa8123-8-2016

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On the Brauer-Manin obstruction for degree-four del Pezzo surfaces

Abstract

Keywords

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