The brauer group of an abelian variety over a finite field

Yu G. Zarkhin

doi:10.1070/IM1983v020n02ABEH001348

The brauer group of an abelian variety over a finite field

Yu G. Zarkhin

Mathematics

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4 Scopus citations

Abstract

The author presents a formula for the order of a component of the Brauer group of an abelian variety over a finite field, where the order of the component in question is relatively prime to the characteristic of the field. For principally polarized abelian surfaces this formula becomes the well-known Artin-Tate formula. A natural nondegenerate pairing between the components of the Brauer groups of an abelian variety and its Picard variety is constructed.Bibliography: 27 titles.

Original language	English (US)
Pages (from-to)	203-234
Number of pages	32
Journal	Mathematics of the USSR - Izvestija
Volume	20
Issue number	2
DOIs	https://doi.org/10.1070/IM1983v020n02ABEH001348
State	Published - Apr 30 1983

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1070/IM1983v020n02ABEH001348

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AB - The author presents a formula for the order of a component of the Brauer group of an abelian variety over a finite field, where the order of the component in question is relatively prime to the characteristic of the field. For principally polarized abelian surfaces this formula becomes the well-known Artin-Tate formula. A natural nondegenerate pairing between the components of the Brauer groups of an abelian variety and its Picard variety is constructed.Bibliography: 27 titles.

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The brauer group of an abelian variety over a finite field

Abstract

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