Non-abelian Chabauty and the Selmer Section Conjecture

Speaker

  • Martin Lüdtke
    University of Groningen

Contatti

Martin Lüdtke, University of Groningen
Non-abelian Chabauty and the Selmer Section Conjecture

Abstract
For a smooth projective curve X/Q of genus at least two, the set of rational points X(Q) is finite by Faltings's Theorem. Grothendieck's Section Conjecture predicts a description of the set X(Q) in terms of Galois sections of the étale fundamental group of X. Another conjectural description is provided by Kim's Conjecture which states that the subset of the p-adic points X(Q_p) computed by the non-abelian Chabauty method agrees with X(Q). I present joint work with A. Betts and T. Kumpitsch relating the two conjectures and verifying them in the case of the thrice-punctured line over Z[1/2].