17 papers · 1 filter
A note on Bremner's conjecture and uniformity
Natalia Garcia-Fritz, Hector Pasten
In 1998, Bremner conjectured that elliptic curves over the rationals having long sequences of distinct rational points whose -coordinates are in arithmetic progression, have lar…
Patterns on elliptic curves beyond Bremner's conjecture
Natalia Garcia-Fritz, Hector Pasten
In the late 1990's, Bremner conjectured that long arithmetic progressions among the -coordinates of rational points of an elliptic curve over should force the r…
Towards Lang--Vojta via Degeneration
Ryan C. Chen, Natalia Garcia-Fritz, Siddharth Mathur +1
Towards the Lang--Vojta conjecture, we prove results on finiteness and Zariski degeneracy of -integral points of varieties over number fields , including many cases with geom…
Xeric varieties
Natalia Garcia-Fritz, Hector Pasten
Let be a smooth projective variety over a number field . The Green--Griffiths--Lang conjecture relates the question of finiteness of rational points in to the triviality…
Effective Mordell for curves with enough automorphisms
Natalia Garcia-Fritz, Hector Pasten
We prove a completely explicit and effective upper bound for the Néron--Tate height of rational points of curves of genus at least over number fields, provided that they have e…
A criterion for non-density of integral points
Natalia Garcia-Fritz, Hector Pasten
We give a general criterion for Zariski degeneration of integral points in the complement of a divisor with components in a variety of dimension defined over $\mathbb{Q…