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Fibered threefolds and Lang-Vojta's conjecture over function fields


Author: Amos Turchet
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14G40; Secondary 11G50
DOI: https://doi.org/10.1090/tran/6968
Published electronically: May 30, 2017
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Abstract: Using the techniques introduced by Corvaja and Zannier in 2008 we solve the non-split case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane. In this situation we deal with sections of an affine threefold fibered over a curve, whose boundary, in the natural projective completion, is a quartic bundle over the base whose fibers have three irreducible components. We prove that the image of each section has bounded degree in terms of the Euler characteristic of the base curve.


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Additional Information

Amos Turchet
Affiliation: Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden
Address at time of publication: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: aturchet@uw.edu

DOI: https://doi.org/10.1090/tran/6968
Keywords: Vojta's conjecture, function fields, fibered threefolds, heights, $S$-units
Received by editor(s): July 2, 2015
Received by editor(s) in revised form: January 26, 2016
Published electronically: May 30, 2017
Article copyright: © Copyright 2017 American Mathematical Society