15 citations · 56 across the 25 of their papers we have counts for
8 papers · 1 filter
Integral torsion points on abelian varieties over function fields
Robin de Jong, Nicole Looper, Farbod Shokrieh
We prove an analogue, over global function fields, of a conjecture due to Su-Ion Ih concerning the non-Zariski density of torsion points on abelian varieties that are integral with…
On the height of Gross-Schoen cycles in genus three
Robin de Jong
We show that there exists a sequence of genus three curves defined over the rationals in which the height of a canonical Gross-Schoen cycle tends to infinity.
Néron-Tate heights of cycles on jacobians
Robin de Jong
We develop a method to calculate the Néron-Tate height of tautological integral cycles on jacobians of curves defined over number fields. As examples we obtain closed expressions f…
Canonical heights and division polynomials
Robin de Jong, J. Steffen Müller
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, n…
Local heights on Galois covers of the projective line
Robin de Jong
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…
Computational aspects of modular forms and Galois representations
Bas Edixhoven, Jean-Marc Couveignes, Robin de Jong +2
This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fi…
On the Arakelov theory of elliptic curves
Robin de Jong
This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic arithmetic surfaces a…
Arakelov invariants of Riemann surfaces
Robin de Jong
We derive explicit formulas for the Arakelov-Green function and the Faltings delta-invariant of a Riemann surface. A numerical example illustrates how these formulas can be used to…