Hector Pasten

activity

20142026

most citedIntersecting the torsion of elliptic curves

1 citations · 1 across the 18 of their papers we have counts for

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Showing 2023Show all

5 papers · 1 filter

math.NT2023

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 $D$ with $n$ components in a variety of dimension $n$ defined over $\mathbb{Q…

math.NT2023

Effectivity for existence of rational points is undecidable

Natalia Garcia-Fritz, Hector Pasten, Xavier Vidaux

The analogue of Hilbert's tenth problem over $Q$ asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as o…

math.LO2023

Hilbert's tenth problem for lacunary entire functions of finite order

Natalia Garcia-Fritz, Hector Pasten

In the context of Hilbert's tenth problem, an outstanding open case is that of complex entire functions in one variable. A negative solution is known for polynomials (by Denef) and…

math.NT2023★ 1 cited

Intersecting the torsion of elliptic curves

Natalia Garcia-Fritz, Hector Pasten

In 2007, Bogomolov and Tschinkel proved that given two complex elliptic curves $E_{1}$ and $E_{2}$ along with even degree- $2$ maps $π_{j} : E_{j} \to P^{1}$ having different bran…

math.NT2023

Propagation of Zariski Dense Orbits

Hector Pasten, Joseph H. Silverman

Let $X / K$ be a smooth projective variety defined over a number field, and let $f : X \to X$ be a morphism defined over $K$ . We formulate a number of statements of varying strengths a…