5 papers
The Chabauty--Coleman method and p-adic linear forms in logarithms
Netan Dogra
Results in -adic transcendence theory are applied to two problems in the Chabauty-Coleman method. The first is a question of McCallum and Poonen regarding repeated roots of Cole…
The local theory of unipotent Kummer maps and refined Selmer schemes
L. Alexander Betts, Netan Dogra
We study the Galois action on paths in the -pro-unipotent étale fundamental groupoid of a hyperbolic curve over a -adic field with . We prove an…
Quadratic Chabauty for modular curves and modular forms of rank one
Netan Dogra, Samuel Le Fourn
In this paper, we provide refined sufficient conditions for the quadratic Chabauty method to produce a finite set of points, with the conditions on the rank of the Jacobian replace…
An effective Chabauty-Kim theorem
Jennifer Balakrishnan, Netan Dogra
The Chabauty--Kim method is a method for finding rational points on curves under certain technical conditions, generalising Chabauty's proof of the Mordell conjecture for curves wi…
Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Jennifer S. Balakrishnan, Netan Dogra, J. Steffen Müller +2
We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compu…