### 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) |
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Pages (from-to) | 203-234 |

Number of pages | 32 |

Journal | Mathematics of the USSR - Izvestija |

Volume | 20 |

Issue number | 2 |

DOIs | |

State | Published - Apr 30 1983 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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*Mathematics of the USSR - Izvestija*, vol. 20, no. 2, pp. 203-234. https://doi.org/10.1070/IM1983v020n02ABEH001348

**The brauer group of an abelian variety over a finite field.** / Zarkhin, Yuriy G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The brauer group of an abelian variety over a finite field

AU - Zarkhin, Yuriy G.

PY - 1983/4/30

Y1 - 1983/4/30

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0039762385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039762385&partnerID=8YFLogxK

U2 - 10.1070/IM1983v020n02ABEH001348

DO - 10.1070/IM1983v020n02ABEH001348

M3 - Article

AN - SCOPUS:0039762385

VL - 20

SP - 203

EP - 234

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 2

ER -