On the algebraic Brauer classes on open degree four del Pezzo surfaces

Jörg Jahnel; Damaris Schindler

doi:10.1016/j.jnt.2019.01.010

On the algebraic Brauer classes on open degree four del Pezzo surfaces

Jörg Jahnel, Damaris Schindler

University of Siegen

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

Abstract

We study the algebraic Brauer classes on open del Pezzo surfaces of degree 4. I.e., on the complements of geometrically irreducible hyperplane sections of del Pezzo surfaces of degree 4. We show that the 2-torsion part is generated by classes of two different types. Moreover, there are two types of 4-torsion classes. For each type, we discuss methods for the evaluation of such a class at a rational point over a p-adic field.

Original language	English
Pages (from-to)	376-427
Number of pages	52
Journal	Journal of Number Theory
Volume	203
DOIs	https://doi.org/10.1016/j.jnt.2019.01.010
Publication status	Published - 1 Oct 2019

Keywords

Algebraic Brauer class
Corestriction
Explicit evaluation of Brauer classes
Non-cyclic Brauer class
Open del Pezzo surface of degree 4
Restriction

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10.1016/j.jnt.2019.01.010

1-s2.0-S0022314X19300496-mainFinal published version, 902 KBLicence: Taverne

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AB - We study the algebraic Brauer classes on open del Pezzo surfaces of degree 4. I.e., on the complements of geometrically irreducible hyperplane sections of del Pezzo surfaces of degree 4. We show that the 2-torsion part is generated by classes of two different types. Moreover, there are two types of 4-torsion classes. For each type, we discuss methods for the evaluation of such a class at a rational point over a p-adic field.

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KW - Corestriction

KW - Explicit evaluation of Brauer classes

KW - Non-cyclic Brauer class

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KW - Restriction

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On the algebraic Brauer classes on open degree four del Pezzo surfaces

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Keywords

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