Related papers: N\'eron-Tate heights of cycles on jacobians

It was shown by Faltings and Hriljac that the N\'eron-Tate height of a point on the Jacobian of a curve can be expressed as the self-intersection of a corresponding divisor on a regular model of the curve. We make this explicit and use it…

We prove a formula, which, given a principally polarized abelian variety $(A,\lambda)$ over the field of algebraic numbers, relates the stable Faltings height of $A$ with the N\'eron--Tate height of a symmetric theta divisor on $A$. Our…

We establish an explicit lower bound for the N\'eron-Tate height on elliptic curves with complex multiplication, for nontorsion points defined over the maximal abelian extension of a number field. Building on a strategy developed by…

We give a close formula for the N\'eron-Tate height of tautological integral cycles on Jacobians of curves over number fields as well as a new lower bound for the arithmetic self-intersection number $\hat{\omega}^2$ of the dualizing sheaf…

We prove a completely explicit and effective upper bound for the N\'eron--Tate height of rational points of curves of genus at least $2$ over number fields, provided that they have enough automorphisms with respect to the Mordell--Weil rank…

We describe a general algorithm for computing intersection pairings on arithmetic surfaces. We have implemented our algorithm for curves over $\mathbb Q$, and we show how to use it to compute regulators for a number of Jacobians of smooth…

We use Arakelov theory to define a height on divisors of degree zero on a hyperelliptic curve over a global field, and show that this height has computably bounded difference from the N\'eron-Tate height of the corresponding point on the…

We define an algebraic analogue, in the case of jacobians of curves, of the height jump divisor introduced recently by R. Hain. We give explicit combinatorial formulae for the height jump for families of semistable curves using labelled…

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…

We obtain explicit, computable upper bounds for the Neron-Tate height of rational points on curves of genus at least two over number fields. The bounds use automorphisms acting on the Mordell-Weil lattice of the Jacobian. We prove an…

In this article, we study Lehmer-type bounds for the N\'eron-Tate height of $\bar{K}$-points on abelian varieties $A$ over number fields $K$. Then, we estimate the number of $K$-rational points on $A$ with N\'eron-Tate height $\leq \log B$…

N\'eron models of abelian varieties do not necessarily exist if the base $S$ has dimension higher than 1. We introduce a new condition, called toric additivity, on a family of smooth curves having nodal reduction over a normal crossing…

The jacobian of the universal curve over $\mathcal{M}_{g,n}$ is an abelian scheme over $\mathcal{M}_{g,n}$. Our main result is the construction of an algebraic space $\beta\colon \tilde{\mathcal{M}}_{g,n} \rightarrow…

Let $E$ be an elliptic curve defined over a number field $K$ with fixed non-archimedean absolute value $v$ of split-multiplicative reduction, and let $f$ be an associated Latt\`es map. Baker proved in 2003 that the N\'eron-Tate height on…

Let A be the jacobian variety of a hyperelliptic curve defined over a number field k. We provide a decomposition formula for the Faltings height of A and for the N\'eron-Tate height of k-rational points on A. We formulate a question of…

This paper contains results concerning a conjecture made by Lang and Silverman predicting a lower bound for the canonical height on abelian varieties of dimension 2 over number fields. The method used here is a local height decomposition.…

We discuss canonical local heights on abelian varieties over non-archimedean fields from the point of view of Berkovich analytic spaces. Our main result is a refinement of N\'eron's classical result relating canonical local heights with…

We prove that the N\'eron-Tate height of subvarieties are always rational numbers. We use the induction formula, and characterize the canonical metric by theta functions.

We consider Tate cycles on an Abelian variety $A$ defined over a sufficiently large number field $K$ and having complex multiplication. We show that there is an effective bound $C = C(A,K)$ so that to check whether a given cohomology class…

We study the essential minimum of the (stable) Faltings height on the moduli space of elliptic curves. We prove that, in contrast to the Weil height on a projective space and the N{\'e}ron-Tate height of an abelian variety, Faltings' height…