Explicit Chabauty-Kim theory for the thrice punctured line in depth 2

Ishai Dan-Cohen, Stefan Wewers

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12 Scopus citations


Let X = P1 / {0, 1,∞}, and let S denote a finite set of prime numbers. In an article of 2005, Kim gave a new proof of Siegel's theorem for X: the set X(Z[S-1]) of S-integral points of X is finite. The proof relies on a 'nonabelian' version of the classical Chabauty method. At its heart is a modular interpretation of unipotent p-adic Hodge theory, given by a tower of morphisms hn between certain Qp-varieties. We set out to obtain a better understanding of h2. Its mysterious piece is a polynomial in 2|S| variables. Our main theorem states that this polynomial is quadratic, and gives a procedure for writing its coefficients in terms of p-adic logarithms and dilogarithms.

Original languageEnglish
Pages (from-to)133-171
Number of pages39
JournalProceedings of the London Mathematical Society
Issue number1
StatePublished - 1 Jan 2015
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)


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