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.
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