Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Looper, Nicole"'
Autor:
Looper, Nicole R.
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. For a polarized dynamical system $X\to X$ over a product formula fie
Externí odkaz:
http://arxiv.org/abs/2404.06981
We prove a dynamical analogue of the Shafarevich conjecture for morphisms $f:\mathbb{P}_K^N\to\mathbb{P}_K^N$ of degree $d\ge2$, defined over a number field $K$. This extends previous work of Silverman and others in the case $N=1$.
Comment: 14 p
Comment: 14 p
Externí odkaz:
http://arxiv.org/abs/2110.13890
Let $K$ be a 1-dimensional function field over an algebraically closed field of characteristic $0$, and let $A/K$ be an abelian surface. Under mild assumptions, we prove a Lehmer-type lower bound for points in $A(\bar{K})$. More precisely, we prove t
Externí odkaz:
http://arxiv.org/abs/2108.09577
Autor:
Looper, Nicole R.
We prove that if $f$ is a polynomial over a number field $K$ with a finite superattracting periodic point and a non-archimedean place of bad reduction, then there is an $\epsilon>0$ such that only finitely many $P\in K^{\text{ab}}$ have canonical hei
Externí odkaz:
http://arxiv.org/abs/2106.13003
Autor:
Looper, Nicole R.
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 arithmetic geometry. Our technique simultaneously yields a dynamical analogue o
Externí odkaz:
http://arxiv.org/abs/2105.05240
We prove that any smooth projective geometrically connected non-isotrivial curve of genus $g\ge 2$ over a one-dimensional function field of any characteristic has at most $16g^2+32g+124$ torsion points for any Abel--Jacobi embedding of the curve into
Externí odkaz:
http://arxiv.org/abs/2101.11593
Autor:
Looper, Nicole
We address the Uniform Boundedness Conjecture of Morton and Silverman in the case of unicritical polynomials, assuming a generalization of the $abc$-conjecture. For unicritical polynomials of degree at least five, we require only the standard $abc$-c
Externí odkaz:
http://arxiv.org/abs/1901.04385
Autor:
Juul, Jamie, Krieger, Holly, Looper, Nicole, Manes, Michelle, Thompson, Bianca, Walton, Laura
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 conditions. We prove a version of Jones' Conjecture for quadratic and cubic
Externí odkaz:
http://arxiv.org/abs/1804.06053
Autor:
Looper, Nicole
We prove that the $abc$-Conjecture implies upper bounds on Zsigmondy sets that are uniform over families of unicritical polynomials over number fields. As an application, we use the $abc$-Conjecture to prove that there exist uniform bounds on the ind
Externí odkaz:
http://arxiv.org/abs/1711.01507
Autor:
Looper, Nicole
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 degree of the polynomial, the degree of the number field, and the number
Externí odkaz:
http://arxiv.org/abs/1709.08121