9 papers
On the Visibility category of the Shafarevich--Tate group
Barinder S. Banwait, Jerson Caro, Shiva Chidambaram
Given an elliptic curve over $\Q$ and a nontrivial element of its Shafarevich--Tate group $\Sha(E)$, we introduce the \textbf{Visualization category} $\V(E; σ)$ of abelian…
Picard rank and Ulrich line bundles on bidouble planes
Jerson Caro, Juan Cruz-Penagos, Sergio Troncoso
We determine the Picard number and the Ulrich complexity of general bidouble covers of the projective plane, providing the first systematic study of Ulrich bundles on non-cyclic ab…
A refined Chabauty--Coleman bound for surfaces
Jennifer S. Balakrishnan, Jerson Caro
Caro and Pasten gave an explicit upper bound on the number of rational points on a hyperbolic surface that is embedded in an abelian variety of rank at most one. We show how to use…
On Diophantine properties for values of Dedekind zeta functions
Jerson Caro, Fabien Pazuki, Riccardo Pengo
We study the Northcott and Bogomolov property for special values of Dedekind -functions at real values . We prove, in particular, that the Bogomolov property is…
Linear -coordinate relations of triples on elliptic curves
Jerson Caro, Natalia Garcia-Fritz
For an elliptic curve defined over the field of complex numbers, we classify all translates of elliptic curves in such that the -coordinates satisfy a lin…
On the fibres of an elliptic surface where the rank does not jump
Jerson Caro, Hector Pasten
For a non-constant elliptic surface over defined over , it is a result of Silverman that the Mordell--Weil rank of the fibres is at least the rank of the…
Watkins's conjecture for quadratic twists of Elliptic Curves with Prime Power Conductor
Jerson Caro
Watkins' conjecture asserts that the rank of an elliptic curve is upper bounded by the -adic valuation of its modular degree. We show that this conjecture is satisfied when …
Watkins' conjecture for elliptic curves over function fields
Jerson Caro
In 2002 Watkins conjectured that given an elliptic curve defined over , its Mordell-Weil rank is at most the -adic valuation of its modular degree. We consider the a…
A Chabauty-Coleman bound for surfaces
Jerson Caro, Hector Pasten
Building on work by Chabauty from 1941, Coleman proved in 1985 an explicit bound for the number of rational points of a curve of genus defined over a number field ,…