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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Counting special points: Logic, diophantine geometry, and transcendence theory


Author: Thomas Scanlon
Journal: Bull. Amer. Math. Soc. 49 (2012), 51-71
MSC (2010): Primary 11G15, 03C64
Published electronically: October 24, 2011
MathSciNet review: 2869007
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Abstract | References | Similar Articles | Additional Information

Abstract: We expose a theorem of Pila and Wilkie on counting rational points in sets definable in o-minimal structures and some applications of this theorem to problems in diophantine geometry due to Masser, Peterzil, Pila, Starchenko, and Zannier.


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Additional Information

Thomas Scanlon
Affiliation: Department of Mathematics, University of California, Berkeley, Evans Hall, Berkeley, California 94720-3840
Email: scanlon@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-2011-01354-4
PII: S 0273-0979(2011)01354-4
Received by editor(s): June 9, 2011
Published electronically: October 24, 2011
Additional Notes: Partially supported by NSF grants FRG DMS-0854998 and DMS-1001550. The author thanks M. Aschenbrenner, J. Pila, P. Tretkoff, and U. Zannier for their detailed comments about earlier versions of these notes.
Article copyright: © Copyright 2011 American Mathematical Society