9 citations · 11 across the 11 of their papers we have counts for
14 papers · 1 filter
Uniform boundedness of small points on abelian varieties over function fields
Nicole Looper, Jit Wu Yap
Let be a field of characteristic and let be the function field of a geometrically irreducible projective curve over . Let be a -dimensional abeli…
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…
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…
A dynamical Shafarevich theorem for endomorphisms of
Jamie Juul, Holly Krieger, Nicole Looper +1
We prove a dynamical analogue of the Shafarevich conjecture for morphisms of degree , defined over a number field . This extends previ…
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…
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…
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 over a one-dimensional function field of any characteristic has at most $16g^2+32…
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…
Dynamical Galois groups of trinomials and Odoni's conjecture
Nicole R. Looper
We prove Odoni's conjecture in all prime degrees; namely, we prove that for every positive prime , there exists a degree polynomial with surjective arbor…
Galois groups of iterates of some unicritical polynomials
Michael R. Bush, Wade Hindes, Nicole R. Looper
We prove that the arboreal Galois representations attached to certain unicritical polynomials have finite index in an infinite wreath product of cyclic groups, and we prove surject…