Vol. 8, No. 5, 2014

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Affine congruences and rational points on a certain cubic surface

Pierre Le Boudec

Vol. 8 (2014), No. 5, 1259–1296
Abstract

We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin’s conjecture for a cubic surface split over $ℚ$ whose singularity type is ${D}_{4}$. This improves on a result of Browning and answers a problem posed by Tschinkel.

Keywords
affine congruences, rational points, Manin's conjecture, cubic surfaces, universal torsors
Primary: 11D45
Secondary: 14G05
Milestones
Received: 30 October 2013
Revised: 5 March 2014
Accepted: 26 April 2014
Published: 16 September 2014
Authors
 Pierre Le Boudec École Polytechnique Fédérale de Lausanne SB MATHGEOM TAN Bâtiment MA Station 8 CH-1015 Lausanne Switzerland