arXiv subjects

F. Pazuki

Publications and source records attributed to F. Pazuki.

3 recordsLinked to original sources

arXiv2015

Décompte dans une conjecture de Lang sur les corps de fonctions : cas des courbes

Let $X$ be a genus $d$ curve with $d\geq 2$ defined over a global function field $K$ of characteristic $p>0$ with $p>2d+1$. Suppose $X$ non-isotrivial. Let $Γ$ be a sub-group of $J(K_s)$, where $J$ is the jacobian of $X$ and $K_s$ is a separable closure of $K$, verifying $Γ/p Γ$ finite. Then one shows that $X\cap Γ$ has finite cardinal and one provides an explicit upper bound. This generalizes a result of Buium and Voloch.

math.NT↗

arXiv2015

Theta height and Faltings height

Using original ideas from J.-B. Bost and S. David, we provide an explicit comparison between the Theta height and the stable Faltings height of a principally polarized abelian variety. We also give as an application an explicit upper bound on the number of K-rational points of a curve of genus g>1 over a number filed K under a conjecture of S. Lang and J. Silverman. We complete the study with a comparison between differential lattice structures.

math.NT↗

arXiv2015

Zhang's conjecture and squares of abelian surfaces

We give in this paper some squares of abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points.

math.NT↗