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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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On the density of rational points on elliptic fibrations

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 1999, Issue 511, Pages 87–93, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.1999.511.87, June 2008

Publication History

Received:
1998-08-31
Accepted:
1998-11-10
Published Online:
2008-06-12

1. Introduction

Let X be an algebraic variety defined over a number field F. We will say that rational points are potentially dense if there exists a finite extension K/F such that the set of K-rational points X(K) is Zariski dense in X. The main problem is to relate this property to geometric invariants of X. Hypothetically, on varieties of general type rational points are not potentially dense. In this paper we are interested in smooth projective varieties such that neither they nor their unramified coverings admit a dominant map onto varieties of general type. For these varieties it seems plausible to expect that rational points are potentially dense (see [2]).

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