Martin Lüdtke (Reichsuniversität Groningen)

For a smooth projective hyperbolic curve over a number field K the set of rational points X(K) is finite by Faltings’ Theorem. Grothendieck’s section conjecture predicts that this set can be described via Galois sections of the étale fundamental group of X. On the other hand, the non-abelian Chabauty method produces p-adic analytic functions which conjecturally cut out X(K) as a subset of X(Q_p). We relate the two conjectures and discuss the example of the thrice-punctured line, where non-abelian Chabauty is used to prove a local-to-glocal principle for the section conjecture.

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