Quadratic points on intersections of two quadrics

Creutz, Brendan; Viray, Bianca

doi:10.2140/ant.2023.17.1411

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Quadratic points on intersections of two quadrics

Brendan Creutz and Bianca Viray

Vol. 17 (2023), No. 8, 1411–1452

DOI: 10.2140/ant.2023.17.1411

Abstract

We prove that a smooth complete intersection of two quadrics of dimension at least $2$ over a number field has index dividing $2$ , i.e., that it possesses a rational $0$ -cycle of degree $2$ .

Keywords

rational points, intersections of quadrics, Brauer–Manin obstruction

Mathematical Subject Classification

Primary: 11D09, 14G05, 14G12

Milestones

Received: 9 September 2021

Revised: 14 July 2022

Accepted: 18 August 2022

Published: 29 August 2023

Authors

Brendan Creutz
School of Mathematics and Statistics University of Canterbury Christchurch New Zealand

Bianca Viray
Department of Mathematics University of Washington Seattle, WA United States

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Vol. 17, No. 8, 2023