• Publications
  • Influence
The number of integral points on arcs and ovals
integral lattice points, and that the exponent and constant are best possible. However, Swinnerton–Dyer [10] showed that the preceding result can be substantially improved if we start with a fixed,Expand
  • 244
  • 57
  • PDF
The rational points of a definable set
Let $X\R^n$ be a set that is definable in an o-minimal structure over $R$. This article shows that in a suitable sense, there are very few rational points of $X$ which do not lie on some connectedExpand
  • 175
  • 31
  • PDF
Rational points in periodic analytic sets and the Manin-Mumford conjecture
We present a new proof of the Manin-Mumford conjecture about torsion points on algebraic subvarieties of abelian varieties. Our principle, which admits other applications, is to view torsion pointsExpand
  • 118
  • 14
  • PDF
Frobenius maps of Abelian varieties and finding roots of unity in finite fields
"If 'twere done when 'tis done, then 'twere well/ It were done quickly."-Macbeth. Abstract. We give a generalization to Abelian varieties over finite fields of the algorithm of Schoof for ellipticExpand
  • 188
  • 9
  • PDF
O-minimality and the André-Oort conjecture for $\mathbb{C}^{n}$
We give an unconditional proof of the Andre-Oort conjecture for arbitrary products of modular curves. We establish two generalizations. The first includes the Manin-Mumford conjecture for arbitraryExpand
  • 132
  • 9
  • PDF
O-minimality and certain atypical intersections
We show that the strategy of point counting in o-minimal structures can be applied to various problems on unlikely intersections that go beyond the conjectures of Manin-Mumford and Andr\'e-Oort. WeExpand
  • 49
  • 9
  • PDF
Rational Points of Definable Sets and Results of André–Oort–Manin–Mumford type
We prove some simple special cases, partly new, of results of Andre-Oort-Manin-Mumford type using an extension to algebraic points of bounded degree of a result of Pila-Wilkie on the density ofExpand
  • 31
  • 8
  • PDF
Density of integral and rational points on varieties
© Société mathématique de France, 1995, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec lesExpand
  • 48
  • 8
  • PDF
Integer points on the dilation of a subanalytic surface
Let � ⊂ R n be a compact subanalytic set of dimension 2 and t 1. This paper gives an upper bound as t →∞ for the number of integer points on the homothetic dilation tofthat do not reside on anyExpand
  • 56
  • 7
  • PDF
On the algebraic points of a definable set
Abstract.This paper studies diophantine properties of sets definable in an o-minimal structure over the real field. The main theorem of the author’s recent paper with A. J. Wilkie is refined, andExpand
  • 42
  • 6
...
1
2
3
4
5
...