On the Brauer group of diagonal quartic surfaces

Evis Ieronymou; Alexei N. Skorobogatov; Yuri G. Zarhin

doi:10.1112/jlms/jdq083

On the Brauer group of diagonal quartic surfaces

Evis Ieronymou
, Alexei N. Skorobogatov
, Yuri G. Zarhin

Mathematics

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

27 Scopus citations

Abstract

We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of ℚ. The proof is based on the isomorphism of the Fermat quartic surface with a Kummer surface due to Mizukami.

Original language	English (US)
Pages (from-to)	659-672
Number of pages	14
Journal	Journal of the London Mathematical Society
Volume	83
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdq083
State	Published - Jun 2011

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/jlms/jdq083

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title = "On the Brauer group of diagonal quartic surfaces",

abstract = "We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of ℚ. The proof is based on the isomorphism of the Fermat quartic surface with a Kummer surface due to Mizukami.",

author = "Evis Ieronymou and Skorobogatov, \{Alexei N.\} and Zarhin, \{Yuri G.\}",

year = "2011",

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doi = "10.1112/jlms/jdq083",

language = "English (US)",

volume = "83",

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journal = "Journal of the London Mathematical Society",

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T1 - On the Brauer group of diagonal quartic surfaces

AU - Ieronymou, Evis

AU - Skorobogatov, Alexei N.

AU - Zarhin, Yuri G.

PY - 2011/6

Y1 - 2011/6

N2 - We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of ℚ. The proof is based on the isomorphism of the Fermat quartic surface with a Kummer surface due to Mizukami.

AB - We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of ℚ. The proof is based on the isomorphism of the Fermat quartic surface with a Kummer surface due to Mizukami.

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UR - https://www.scopus.com/pages/publications/79957512823#tab=citedBy

U2 - 10.1112/jlms/jdq083

DO - 10.1112/jlms/jdq083

M3 - Article

AN - SCOPUS:79957512823

SN - 0024-6107

VL - 83

SP - 659

EP - 672

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

On the Brauer group of diagonal quartic surfaces

Abstract

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