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math.NT2019
Two recent p-adic approaches towards the (effective) Mordell conjecture
Jennifer S. Balakrishnan, Alex J. Best, Francesca Bianchi +4
We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usual…
math.NT2019
Explicit quadratic Chabauty over number fields
Jennifer S. Balakrishnan, Amnon Besser, Francesca Bianchi +1
We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary nu…
math.NT2019
Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture
Francesca Bianchi
We explore a number of problems related to the quadratic Chabauty method for determining integral points on hyperbolic curves. We remove the assumption of semistability in the desc…