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February 2019 Brauer groups of Châtelet surfaces over local fields
Takashi HIROTSU
Hokkaido Math. J. 48(1): 141-154 (February 2019). DOI: 10.14492/hokmj/1550480647

Abstract

A Châtelet surface over a field is a typical geometrically rational surface. Its Chow group of zero-cycles has been studied as an important birational invariant by many researchers since the 1970s. Recently, S. Saito and K. Sato obtained a duality between the Chow and Brauer groups from the Brauer-Manin pairing. For a Châtelet surface over a local field, we combine their result with the known calculation of the Chow group to determine the structure and generators of the Brauer group of a regular proper flat model of the surface over the integer ring of the base field.

Citation

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Takashi HIROTSU. "Brauer groups of Châtelet surfaces over local fields." Hokkaido Math. J. 48 (1) 141 - 154, February 2019. https://doi.org/10.14492/hokmj/1550480647

Information

Published: February 2019
First available in Project Euclid: 18 February 2019

zbMATH: 1409.14044
MathSciNet: MR3914172
Digital Object Identifier: 10.14492/hokmj/1550480647

Subjects:
Primary: 14G20
Secondary: 14C15, 14F22, 14J26

Rights: Copyright © 2019 Hokkaido University, Department of Mathematics

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Vol.48 • No. 1 • February 2019
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