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David Corwin: Beyond Quadratic Chabauty: Explicit Motivic Non-Abelian Chabauty for Elliptic Curves

NOTE: SPECIAL TIME

Time: Wed 2020-10-28 15.15 - 16.15

Location: Zoom, meeting ID: 657 9019 8929

Lecturer: David Corwin, Berkeley-MSRI

Abstract

We describe ongoing joint work with Ishai Dan-Cohen and Stefan Wewers to apply explicit versions of the non-abelian Chabauty's method of Minhyong Kim to new situations. The eventual goal is a conjectural algorithm for provably finding the set of rational points on a hyperbolic algebraic curve.

Faltings' Theorem states that every hyperbolic (i.e., of genus at least 2) algebraic curve X has finitely many rational points, but there is no known algorithm for provably finding the set of rational points. The non-abelian Chabauty's method of Kim led to new progress in this direction, in particular via the Quadratic Chabauty method of Balakrishnan and others, corresponding to simplest non-abelian nilpotent quotient of the fundamental group of X. We explain recent and ongoing progress toward doing computations for a larger non-abelian quotient of the fundamental group. The approach is based on previous work of Dan-Cohen--Wewers and C--Dan-Cohen using explicit functions on a Tannakian Galois group.

Zoom Notes: The meeting ID is 657 9019 8929 and the passcode is 3517257.

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Last changed: Oct 23, 2020