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Points of Small Height on Varieties Defined over a Function Field

Published online by Cambridge University Press:  20 November 2018

Dragos Ghioca
Dragos Ghioca*
Affiliation:
Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada
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Abstract

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We obtain a Bogomolov type of result for the affine space defined over the algebraic closure of a function field of transcendence degree 1 over a finite field.

Keywords

11G5011G2511G10heightsBogomolov conjecture
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 2 , 01 June 2009 , pp. 237 - 244
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Bilu, Y., Limit distribution of small points on algebraic tori. Duke Math. J. 89(1997), no. 3, 465–476.Google Scholar
[2] Bombieri, E. and Zannier, U., Algebraic points on subvarieties of . Internat. Math. Res. Notices 1995, no. 7, 333–347.Google Scholar
[3] Bosser, V., Transcendance et approximation diophantienne sur les modules de Drinfeld.. Ph.D. Thesis, Université de Paris 06, 2000.Google Scholar
[4] Bosser, V., Hauteurs normalisées des sous-variétés de produits de modules de Drinfeld. Compositio Math. 133(2002), no. 3, 323–353.Google Scholar
[5] David, S. and Philippon, P., Sous-variétés de torsion des variétés semi-abéliennes. C. R. Acad. Sci. Paris Sér. I Math. 331(2000), no. 8, 587–592.Google Scholar
[6] Ghioca, D., Equidistribution for torsion points of a Drinfeld module. Math. Ann. 336(2006), no. 4, 841–865.Google Scholar
[7] Moriwaki, A., Arithmetic height functions on finitely generated fields. Invent. Math 140(2000), no. 1, 101–142.Google Scholar
[8] Raynaud, M., Sous-variétés d’une variété abélienne et points de torsion. In: Arithmetic and geometry, Vol. I, Prog. Math. 35, Birkhauser boston, Boston, MA, 1983, pp. 327–352.Google Scholar
[9] Serre, J.-P., Lectures on the Mordell–Weil theorem. Third edition. Aspects of Mathematics. Friedr. Vieweg and Sohn, Braunschweig, 1997.Google Scholar
[10] Ullmo, E., Positivité et discrétion des points algébriques des courbes. Ann. of Math. (2) 147(1998), no. 1, 167–179.Google Scholar
[11] Zhang, S., Positive line bundles on arithmetic varieties. J. Amer. Math. Soc. 8(1995), no. 1, 187–221.Google Scholar
[12] Zhang, S., Equidistribution of small points on abelian varieties. Ann. of Math. (2) 147(1998), no. 1, 159–165.Google Scholar