50 citations · 79 across the 15 of their papers we have counts for
19 papers
Arithmetic jet spaces and the unramified Zilber--Pink conjecture for subvarieties of abelian varieties
Netan Dogra, Arnab Saha
We show how the methods of delta geometry can be used to bound the degree of points in the Zilber--Pink locus of a subvariety of an abelian variety, if the varieties are defined ov…
Ockhamareto: Pareto-Gated Segment-Level Credit Assignment for Concise Unit-Test Generation with Reinforcement Learning
Dong Huang, Mark Harman, Jie M. Zhang +3
We introduce \textbf{Ockhamareto}, a single-shot GRPO framework for unit-test generation and selection, based on the principles of \emph{Ockham's Razor} and \emph{Pareto Optimality…
p-adic elliptic polylogarithms and cubic Chabauty
Jennifer S. Balakrishnan, Francesca Bianchi, Netan Dogra
The Chabauty--Coleman--Kim method, under favourable circumstances, describes the set of integral points of a hyperelliptic curve inside the -adic zeroes of certain transcendenta…
Generalised height pairings and the Albanese kernel
Netan Dogra
The Chabauty--Coleman--Kim method in depth two describes the rational points on a curve in terms of a generalisation of Nekovář's -adic height pairing which replaces $\mathbb{G}…
-adic approaches to unlikely intersections
Netan Dogra
In this article we explain the Buium--Coleman approach to the Manin--Mumford conjecture, and outline its generalisations. As an illustration, we give a -adic proof of a theorem…
A Buium--Coleman bound for the Mordell--Lang conjecture
Netan Dogra, Sudip Pandit
For a hyperbolic curve of genus with good reduction at , we give an explicit bound on the Mordell--Lang locus , when …
2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II
Netan Dogra
We give refined methods for proving finiteness of the Chabauty--Coleman--Kim set , when is a hyperelliptic curve with a rational Weierstrass point. The mai…
The Zilber--Pink conjecture for products of curves with highly degenerate reduction
Netan Dogra
We give a proof of the Zilber--Pink conjecture for -fold self-products of a curve inside the self-product of its Jacobian, when has appropriate bad reduction, its Jacobi…
2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I
Netan Dogra
This paper introduces explicit Galois cohomological methods for determining the ranks of Bloch--Kato Selmer groups associated to the Tate twists of the 2-adic second étale cohomolo…
p-adic integrals and linearly dependent points on families of curves I
Netan Dogra
We prove that the set of `low rank' points on sufficiently large fibre powers of families of curves are not Zariski dense. The recent work of Dimitrov-Gao-Habegger and Kühne (and Y…
Quadratic Chabauty for modular curves: Algorithms and examples
Jennifer S. Balakrishnan, Netan Dogra, Jan Steffen Müller +2
We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rational points on modular curves of genus whose Jacobians have Mordell--Weil…
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…
Unlikely intersections and the Chabauty-Kim method over number fields
Netan Dogra
The Chabauty--Kim method is a tool for finding the integral or rational points on varieties over number fields via certain transcendental -adic analytic functions arising from c…
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…
Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties
Jennifer S. Balakrishnan, Netan Dogra
We give new instances where Chabauty--Kim sets can be proved to be finite, by developing a notion of "generalised height functions" on Selmer varieties. We also explain how to comp…
Quadratic Chabauty and rational points I: p-adic heights
Jennifer S. Balakrishnan, Netan Dogra
We give the first explicit examples beyond the Chabauty-Coleman method where Kim's nonabelian Chabauty program determines the set of rational points of a curve defined over $\mathb…