Uniformity in Mordell–Lang for curves
V Dimitrov, Z Gao, P Habegger - Annals of Mathematics, 2021 - projecteuclid.org
Consider a smooth, geometrically irreducible, projective curve of genus g≥2 defined over a
number field of degree d≥1. It has at most finitely many rational points by the Mordell …
number field of degree d≥1. It has at most finitely many rational points by the Mordell …
Uniform Manin-Mumford for a family of genus 2 curves
L DeMarco, H Krieger, H Ye - Annals of Mathematics, 2020 - projecteuclid.org
We introduce a general strategy for proving quantitative and uniform bounds on the number
of common points of height zero for a pair of inequivalent height functions on P^1(Q). We …
of common points of height zero for a pair of inequivalent height functions on P^1(Q). We …
Hodge theory for tropical varieties
O Amini, M Piquerez - arXiv preprint arXiv:2007.07826, 2020 - arxiv.org
In this paper we prove that the cohomology of smooth projective tropical varieties verify the
tropical analogs of three fundamental theorems which govern the cohomology of complex …
tropical analogs of three fundamental theorems which govern the cohomology of complex …
Equidistribution in families of abelian varieties and uniformity
L Kühne - arXiv preprint arXiv:2101.10272, 2021 - arxiv.org
Using equidistribution techniques from Arakelov theory as well as recent results obtained by
Dimitrov, Gao, and Habegger, we deduce uniform results on the Manin-Mumford and the …
Dimitrov, Gao, and Habegger, we deduce uniform results on the Manin-Mumford and the …
Degeneration of linear series from the tropical point of view and applications
M Baker, D Jensen - Nonarchimedean and tropical geometry, 2016 - Springer
We discuss linear series on tropical curves and their relation to classical algebraic geometry,
describe the main techniques of the subject, and survey some of the recent major …
describe the main techniques of the subject, and survey some of the recent major …
Tropical independence, II: The maximal rank conjecture for quadrics
D Jensen, S Payne - Algebra & Number Theory, 2016 - msp.org
Building on our earlier results on tropical independence and shapes of divisors in tropical
linear series, we give a tropical proof of the maximal rank conjecture for quadrics. We also …
linear series, we give a tropical proof of the maximal rank conjecture for quadrics. We also …
[图书][B] Point-Counting and the Zilber–Pink Conjecture
J Pila - 2022 - books.google.com
Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil rank.
M Stoll - Journal of the European Mathematical Society (EMS …, 2019 - ems.press
We show that there is a bound depending only on g, r and [K: Q] for the number of K-rational
points on a hyperelliptic curve C of genus g over a number field K such that the Mordell–Weil …
points on a hyperelliptic curve C of genus g over a number field K such that the Mordell–Weil …
Limit linear series: combinatorial theory
O Amini, L Gierczak - arXiv preprint arXiv:2209.15613, 2022 - arxiv.org
The aim of this paper is to develop a purely combinatorial theory of limit linear series on
metric graphs. This will be based on the formalism of hypercube rank functions and slope …
metric graphs. This will be based on the formalism of hypercube rank functions and slope …