Nicole R. Looper

activity

20242026

collaborators

5 papers

math.NT2026

Uniform boundedness of small points on abelian varieties over function fields

Nicole Looper, Jit Wu Yap

Let $k$ be a field of characteristic $0$ and let $K = k (B)$ be the function field of a geometrically irreducible projective curve $B$ over $k$ . Let $A / K$ be a $g$ -dimensional abeli…

math.NT2026

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…

math.NT2026

A uniform quantitative Manin-Mumford theorem for curves over function fields

Nicole Looper, Joseph Silverman, Robert Wilms

We prove that any smooth projective geometrically connected non-isotrivial curve of genus $g \geq 2$ over a one-dimensional function field of any characteristic has at most $16g^2+32…

math.NT2025

The Uniform Boundedness and Dynamical Lang Conjectures for polynomials

Nicole R. Looper

We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmeti…

math.NT2024

Arakelov-Green's functions for dynamical systems on projective varieties

Nicole R. Looper

We introduce functions associated to polarized dynamical systems that generalize averages of the dynamical Arakelov-Green's functions for rational functions due to Baker and Rumely…