Let\ua0X\ua0⊂ ℙn\ua0be a projective geometrically integral variety over of dimension\ua0r\ua0and degree\ua0d\ua0≧ 4. Suppose that there are only finitely many (r\ua0− 1)-planes over\ua0 \ua0on\ua0X. The main result of this paper is a proof of the fact that the number\ua0N(X;B) of rational points on\ua0Xwhich have height at most\ua0B\ua0satisfies\ua0 \ua0for any ɛ > 0. The implied constant depends at most on\ua0d,\ua0n\ua0and ɛ
For any $n \geq 2$, let $F \in \mathbb{Z}[x_1,\ldots,x_n]$ be a form of degree $d\geq 2$, which prod...
For any n ≧ 2, let F ε ℤ[x1, . . . , xn] be a form of degree d ≧ 2, which produces a geometrically i...
This book is intended to be an introduction to Diophantine geometry. The central theme of the book i...
For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is...
For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is...
Let K be a number eld, S a nite set of valuations of K, including the archimedean valuations, and O ...
This thesis presents various results concerning the density of rational and integral points on algeb...
We determine an asymptotic formula for the number of integral points of bounded height on a certain ...
We give upper bounds for the number of rational points of bounded height on the complement of the li...
The Vojta’s conjecture establishes geometrical conditions on the degeneracy of the set of S-integra...
International audienceWe give an upper bound on the number of rational points of an arbitrary Zarisk...
International audienceWe give an upper bound on the number of rational points of an arbitrary Zarisk...
International audienceWe give an upper bound on the number of rational points of an arbitrary Zarisk...
This book is intended to be an introduction to Diophantine geometry. The central theme of the book i...
One says that an algebraic variety V defined over a field K has po-tential density of rational point...
For any $n \geq 2$, let $F \in \mathbb{Z}[x_1,\ldots,x_n]$ be a form of degree $d\geq 2$, which prod...
For any n ≧ 2, let F ε ℤ[x1, . . . , xn] be a form of degree d ≧ 2, which produces a geometrically i...
This book is intended to be an introduction to Diophantine geometry. The central theme of the book i...
For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is...
For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is...
Let K be a number eld, S a nite set of valuations of K, including the archimedean valuations, and O ...
This thesis presents various results concerning the density of rational and integral points on algeb...
We determine an asymptotic formula for the number of integral points of bounded height on a certain ...
We give upper bounds for the number of rational points of bounded height on the complement of the li...
The Vojta’s conjecture establishes geometrical conditions on the degeneracy of the set of S-integra...
International audienceWe give an upper bound on the number of rational points of an arbitrary Zarisk...
International audienceWe give an upper bound on the number of rational points of an arbitrary Zarisk...
International audienceWe give an upper bound on the number of rational points of an arbitrary Zarisk...
This book is intended to be an introduction to Diophantine geometry. The central theme of the book i...
One says that an algebraic variety V defined over a field K has po-tential density of rational point...
For any $n \geq 2$, let $F \in \mathbb{Z}[x_1,\ldots,x_n]$ be a form of degree $d\geq 2$, which prod...
For any n ≧ 2, let F ε ℤ[x1, . . . , xn] be a form of degree d ≧ 2, which produces a geometrically i...
This book is intended to be an introduction to Diophantine geometry. The central theme of the book i...
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