Related papers: Canonical heights for correspondences

This paper is the sequel of our paper "Arithmetic height functions over finitely generated fields" (cf. math.NT/9809016). In this paper, we define the canonical height of subvarieties of an abelian variety over a finitely generated field…

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 show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.

We study canonical heights for plane polynomial mappings of small topological degree. In particular, we prove that for points of canonical height zero, the arithmetic degree is bounded by the topological degree and hence strictly smaller…

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…

Let X be a smooth projective curve of positive genus defined over a number field K. Assume given a Galois covering map x from X to the projective line over K and a place v of K. We introduce a local canonical height on the set of K_v-valued…

We present the construction of canonical lifts of $\ell$-adic cycle classes of sections of $p$-adic projective anabelian curves to the cohomology of arbitrary proper, regular, flat models. This answers a question of Esnault and Wittenberg.

Let A be an abelian variety defined over a number field K, and consider the canonical height function attached to a symmetric ample line bundle L on A. We prove that there is a positive lower bound C (depending on A, K, and L) for the…

For several applications in the arithmetic of abelian varieties it is important to compute canonical heights. Following Faltings and Hriljac, we show how the canonical height on the Jacobian of a smooth projective curve can be computed…

Let K be a function field in one variable over an arbitrary field F. Given a rational function f(z) in K(z) of degree at least two, the associated canonical height on the projective line was defined by Call and Silverman. The preperiodic…

We define arithmetical and dynamical degrees for dynamical systems with several rational maps on projective varieties, study their properties and relations, and prove the existence of a canonical height function associated with divisorial…

We discuss a new method to compute the canonical height of an algebraic point on a hyperelliptic jacobian over a number field. The method does not require any geometrical models, neither $p$-adic nor complex analytic ones. In the case of…

Let K be an algebraic number field. For a degree d rational morphism of projective n-space defined over K let R denote its minimal resultant ideal. For a fixed height function on the moduli space of dynamical systems this paper shows that…

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…

Let f : X --> X be an endomorphism of a normal projective variety defined over a global field K, and let D_0,D_1,D_2,... be divisor classes that form a Jordan block with eigenvalue b for the action of f^* on Pic(X) tensored with C. We…

An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic…

A polarizable endomorphism on a projective variety enables us to consider given morphism as constant multiplication in the height function. In this paper, we will generalize it for arbitrary dominant endomorphism by defining the height…

Let (X,D) be a projective log pair over the ring of integers of a number field such that the log canonical line bundle K_(X,D) or its dual -K_(X,D) is relatively ample. We introduce a canonical height of K_(X,D) (and -K(X,D)) which is…

We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along…

We present an explicit expression for the normalized height of a projective toric variety. This expression decomposes as a sum of local contributions, each term being the integral of a certain function, concave and piecewise linear-affine.…