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

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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.}",

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AU - Ieronymou, Evis

AU - Skorobogatov, Alexei N.

AU - Zarhin, Yuri G.

PY - 2011/6

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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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On the Brauer group of diagonal quartic surfaces

Abstract

All Science Journal Classification (ASJC) codes

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