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Thirteenth Algorithmic Number Theory Symposium ANTS-XIII
University of Wisconsin, Madison
July 16 – 20, 2018

Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII)
July 16 – 20, 2018

Effective aspects of quadratic Chabauty

Jennifer Balakrishnan

Abstract: Let C be a smooth projective curve with genus at least 2 defined over the rational numbers. It was conjectured by Mordell and proved by Faltings that C has finitely many rational points. However, Faltings' proof does not give an algorithm for finding these points.

In the case when the Jacobian of C has rank less than its genus, the Chabauty-Coleman method can often be used to find the rational points of C, using the construction of certain p-adic line integrals. In certain cases of higher rank, p-adic heights can often be used to find rational or integral points on C. I will describe these "quadratic Chabauty" techniques (part of Kim's nonabelian Chabauty program), based on joint work with Amnon Besser, Netan Dogra, Steffen Mueller, Jan Tuitman, and Jan Vonk.

Files available: slides

© 2017-2018 Jennifer Paulhus (with thanks to Kiran S. Kedlaya, and by extension Pierrick Gaudry and Emmanuel Thomé)