Local heights on Abelian varieties and rigid analytic uniformization.
Local heights on Galois covers of the projective line
Lower Bounds for Heights on Finitely Generated Groups.
Lower bounds on the projective heights of algebraic points
Manin’s conjecture for a singular sextic del Pezzo surface
We prove Manin’s conjecture for a del Pezzo surface of degree six which has one singularity of type . Moreover, we achieve a meromorphic continuation and explicit expression of the associated height zeta function.
Manin's conjecture for two quartic del Pezzo surfaces with 3A₁ and A₁ + A₂ singularity types
Minimum essentiel et degrés d'obstruction des translatés de sous-tores
Minoration de la hauteur normalisée des hypersurfaces
1. Introduction. Dans un article célèbre, D. H. Lehmer posait la question suivante (voir [Le], §13, page 476): «The following problem arises immediately. If ε is a positive quantity, to find a polynomial of the form: where the a’s are integers, such that the absolute value of the product of those roots of f which lie outside the unit circle, lies between 1 and 1 + ε (...). Whether or not the problem has a solution for ε < 0.176 we do not know.» Cette question, toujours ouverte, est la source...
Minoration effective de la hauteur des points d’une courbe de définie sur ℚ
Minorations des hauteurs normalisées des sous-variétés des tores
Multiplicative independence and bounded height
Numerical characterization of nef arithmetic divisors on arithmetic surfaces
In this paper, we give a numerical characterization of nef arithmetic -Cartier divisors of -type on an arithmetic surface. Namely an arithmetic -Cartier divisor of -type is nef if and only if is pseudo-effective and .
On heights of multiplicatively dependent algebraic numbers
On Manin's conjecture for a certain singular cubic surface
On the average value of the canonical height in higher dimensional families of elliptic curves
Given an elliptic curve E over a function field K = ℚ(T₁,...,Tₙ), we study the behavior of the canonical height of the specialized elliptic curve with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient over all nontorsion P ∈ E(K).
On the distribution of rational points on certain Kummer surfaces
On the height constant for curves of genus two
On the height constant for curves of genus two, II
On the height of algebraic numbers with real conjugates
On the height of the Sylvester resultant.