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The Brauer–Manin obstruction for integral points on curves

Published online by Cambridge University Press:  24 June 2010

DAVID HARARI  and
JOSÉ FELIPE VOLOCH
DAVID HARARI
Affiliation:
Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, Orsay Cedex, F-91405, France. e-mail: david.harari@math.u-psud.fr
JOSÉ FELIPE VOLOCH
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712, U.S.A. e-mail: voloch@math.utexas.edu
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Abstract

We discuss the question of whether the Brauer–Manin obstruction is the only obstruction to the Hasse principle for integral points on affine hyperbolic curves. In the case of rational curves we conjecture a positive answer, we prove that this conjecture can be given several equivalent formulations and we relate it to an old conjecture of Skolem. Finally, we show that for elliptic curves minus one point a strong version of the question (describing the set of integral points by local conditions) has a negative answer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 3 , November 2010 , pp. 413 - 421
Copyright
Copyright © Cambridge Philosophical Society 2010

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