New York Journal of Mathematics
Volume 18 (2012) 291-293


Ricardo Conceição, Douglas Ulmer, and José Felipe Voloch

Unboundedness of the number of rational points on curves over function fields

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Published: April 26, 2012
Keywords: Algebraic curves, function fields, rational points
Subject: 11G30

We construct sequences of smooth nonisotrivial curves of every genus at least two, defined over a rational function field of positive characteristic, such that the (finite) number of rational points of the curves in the sequence cannot be uniformly bounded.

Author information

Ricardo Conceição:
Department of Mathematics, Oxford College of Emory University, Oxford, GA 30054, USA

Douglas Ulmer:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA

José Felipe Voloch:
Department of Mathematics, University of Texas, Austin, TX 78712, USA