The local theory of unipotent Kummer maps and refined Selmer schemes

2019/09/12 by Betts, L. Alexander, Dogra, Netan · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.05734

Abstract

We study the Galois action on paths in the ℚ_ℓ-pro-unipotent étale fundamental groupoid of a hyperbolic curve X over a p-adic field with ℓ≠ p. We prove an Oda--Tamagawa-type criterion for the existence of a Galois-invariant path in terms of the reduction of X, as well as an anabelian reconstruction result determining the stable reduction type of X in terms of its fundamental groupoid. We give an explicit combinatorial description of the non-abelian Kummer map of X in arbitrary depth, and deduce consequences for the non-abelian Chabauty method for affine hyperbolic curves and for explicit quadratic Chabauty.

Cited by

• Affine Chabauty I

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