Cohomology and the Brauer groups of diagonal surfaces

Gvirtz, D. and Skorobogatov, A. N. (2022) Cohomology and the Brauer groups of diagonal surfaces. Duke Mathematical Journal, 171(6), pp. 1299-1347. (doi: 10.1215/00127094-2021-0029)

Abstract

We present a method for calculating the Brauer group of a surface given by a diagonal equation in projective space. For diagonal quartic surfaces with coefficients in Q, we determine the Brauer groups over Q and Q(i).

• Item Type: Articles
• Additional Information: The first author was supported by EPSRC (grant EP/L015234/1) and the EPSRC Centre for Doctoral Training in Geometry and Number Theory.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Gvirtz, Dr Damian
• Authors: Gvirtz, D., and Skorobogatov, A. N.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Duke Mathematical Journal
• Publisher: Duke University Press
• ISSN: 0012-7094
• ISSN (Online): 1547-7398
• Published Online: 30 March 2022
• Copyright Holders: Copyright © 2022 Duke University Press
• First Published: First published in Duke Mathematical Journal 171(6): 1299-1347
• Publisher Policy: Reproduced in accordance with the publisher copyright policy