• Corpus ID: 235485159

Refined Selmer equations for the thrice-punctured line in depth two

@inproceedings{Best2021RefinedSE,
title={Refined Selmer equations for the thrice-punctured line in depth two},
author={Alex J Best and L. Alexander Betts and Theresa Kumpitsch and Martin Ludtke and Angus McAndrew and Li Qian and Elie Studnia and Yujie Xu},
year={2021}
}
• Published 18 June 2021
• Mathematics
In [Kim05], Kim gave a new proof of Siegel’s Theorem that there are only finitely many S-integral points on PZ \ {0, 1,∞}. One advantage of Kim’s method is that it in principle allows one to actually find these points, but the calculations grow vastly more complicated as the size of S increases. In this paper, we implement a refinement of Kim’s method to explicitly compute various examples where S has size 2 which has been introduced in [BD19]. In so doing, we exhibit new examples of a natural…
1 Citations

The Heisenberg coboundary equation: appendix to Explicit Chabauty-Kim theory

• Mathematics
• 2014
Let p be a regular prime number, let Gp denote the Galois group of the maximal unramified away from p extension of Q, and let H_et denote the Heisenberg group over Qp with Gp-action given by H_et =

The finite nth polylogarithm lin(z) ∈ ℤ/p(z) is defined as ∑k=1p−1zk/kn. We state and prove the following theorem. Let Lik: ℂp → ℂp be the p-adic polylogarithms defined by Coleman. Then a certain

A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves

• Mathematics
Mathematische Annalen
• 2018
Let X denote a hyperbolic curve over $$\mathbb {Q}$$Q and let p denote a prime of good reduction. The third author’s approach to integral points, introduced in Kim (Invent Math 161:629–656, 2005;

Cosimplicial Objects in Algebraic Geometry

Let X be an arc-connected and locally arc-connected topological space and let I be the unit interval. Applying the connected component functor to each fibre of the fibration of the total space map(I,