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

Alex J. Best, L. Alexander Betts, Theresa Kumpitsch, Martin Lüdtke, Angus W. McAndrew, Lie Qian, Elie Studnia, Yujie Xu

Onderzoeksoutput: VoordrukAcademic

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In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many $S$-integral points on $\mathbb P^1_{\mathbb Z}\setminus\{0,1,\infty\}$. 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 generalisation of a conjecture of Kim.
Originele taal-2English
StatusAccepted/In press - 26-jul.-2023

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