6 papers
A Lehmer-type height lower bound for abelian surfaces over function fields
Nicole R. Looper, Joseph H. Silverman
Let be a 1-dimensional function field over an algebraically closed field of characteristic , and let be an abelian surface. Under mild assumptions, we prove a Lehmer-t…
A Bogomolov property for the canonical height of maps with superattracting periodic points
Nicole R. Looper
We prove that if is a polynomial over a number field with a finite superattracting periodic point and a non-archimedean place of bad reduction, then there is an such…
Dynamical uniform boundedness and the -conjecture
Nicole Looper
We address the Uniform Boundedness Conjecture of Morton and Silverman in the case of unicritical polynomials, assuming a generalization of the -conjecture. For unicritical pol…
Arboreal representations for rational maps with few critical points
Jamie Juul, Holly Krieger, Nicole Looper +3
Jones conjectures the arboreal representation of a degree two rational map will have finite index in the full automorphism group of a binary rooted tree except under certain condit…
The -Conjecture implies uniform bounds on dynamical Zsigmondy sets
Nicole Looper
We prove that the -Conjecture implies upper bounds on Zsigmondy sets that are uniform over families of unicritical polynomials over number fields. As an application, we use th…
A lower bound on the canonical height for polynomials
Nicole Looper
We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the deg…