3 papers
math.NT2022
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…
math.NT2022
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…
math.NT2021
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 ,…