Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4

Vladimir Mitankin; Cecília Salgado Guimarães da Silva

doi:10.1016/j.jnt.2021.07.030

Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4

Vladimir Mitankin^*, Cecília Salgado Guimarães da Silva^*

^*Corresponding author for this work

Algebra

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Abstract

We consider a family of smooth del Pezzo surfaces of degree four and study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.

Original language	English
Pages (from-to)	463-478
Number of pages	16
Journal	Journal of Number Theory
Volume	236
Early online date	30-Aug-2021
DOIs	https://doi.org/10.1016/j.jnt.2021.07.030
Publication status	Published - Jul-2022

Keywords

del Pezzo surfaces
Brauer groups
elliptic fibrations

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Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4Final publisher's version, 403 KBLicence: Taverne

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title = "Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4",

abstract = "We consider a family of smooth del Pezzo surfaces of degree four and study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.",

keywords = "del Pezzo surfaces, Brauer groups, elliptic fibrations",

author = "Vladimir Mitankin and {Salgado Guimar{\~a}es da Silva}, Cec{\'i}lia",

year = "2022",

month = jul,

doi = "10.1016/j.jnt.2021.07.030",

language = "English",

volume = "236",

pages = "463--478",

journal = "Journal of Number Theory",

issn = "0022-314X",

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TY - JOUR

T1 - Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4

AU - Mitankin, Vladimir

AU - Salgado Guimarães da Silva, Cecília

PY - 2022/7

Y1 - 2022/7

N2 - We consider a family of smooth del Pezzo surfaces of degree four and study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.

AB - We consider a family of smooth del Pezzo surfaces of degree four and study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.

KW - del Pezzo surfaces

KW - Brauer groups

KW - elliptic fibrations

U2 - 10.1016/j.jnt.2021.07.030

DO - 10.1016/j.jnt.2021.07.030

M3 - Article

SN - 0022-314X

VL - 236

SP - 463

EP - 478

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4

Abstract

Keywords

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