3 citations · 7 across the 4 of their papers we have counts for
4 papers
Specialization of canonical heights on abelian varieties
Alexander Carney
Given a family of abelian varieties over a quasiprojective smooth curve over a global field and a point on the generic fiber, we show that the Néron-Tate canonical height…
Integral points in orbits in characteristic
Alexander Carney, Wade Hindes, Thomas J. Tucker
We prove a characteristic version of a theorem of Silverman on integral points in orbits over number fields and establish a primitive prime divisor theorem for polynomials in t…
Heights and arithmetic dynamics over finitely generated fields
Alexander Carney
We develop a theory of vector-valued heights and intersections defined relative to finitely generated extensions K/k. These generalize both number field and geometric heights. When…
The arithmetic Hodge Index Theorem and rigidity of dynamical systems over function fields
Alexander Carney
In one of the fundamental results of Arakelov's arithmetic intersection theory, Faltings and Hriljac (independently) proved the Hodge Index Theorem for arithmetic surfaces by relat…