Non-abelian Chabauty and the Selmer Section Conjecture
Wednesday 23 October 2024
15:00
Aula Mancini, Palazzo della Carovana
Speaker
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Martin LüdtkeUniversity of Groningen
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].