Affine congruences and rational points on a certain cubic surface

Le Boudec, Pierre

doi:10.2140/ant.2014.8.1259

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Affine congruences and rational points on a certain cubic surface

Pierre Le Boudec

Vol. 8 (2014), No. 5, 1259–1296

DOI: 10.2140/ant.2014.8.1259

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

Mathematical Subject Classification 2010

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

Vol. 8, No. 5, 2014