Local non-abelian Kummer maps for curves

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• Alexander Betts (Max Planck)
• Tuesday 12 March 2019, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Beth Romano.

The non-abelian Kummer map associated to a variety X is a certain function which relates the Diophantine geometry of X to its etale fundamental group, and appears for example in the non-abelian Chabauty method of Minhyong Kim. In this talk, I will outline work in progress with Netan Dogra, providing a completely explicit description of the p-adic non-abelian Kummer map for a curve X over an l-adic field (l different from p) in terms of harmonic analysis on its reduction graph. In particular, we obtain a description of the local components of p-adic height functions on X in terms of the combinatorial height pairing on its reduction graph, thereby removing one of the current limitations on the explicit quadratic Chabauty method of Balakrishnan and Dogra.

This talk is part of the Number Theory Seminar series.

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