Seminario / Viada
On WEDNESDAY November 14th, 16.00-17.00, Aula C
Evelina VIADA (Goettingen) will talk about
"Torsion anomalous Conjecture and Rational Points on Curves"
Abstract: During the last years, together with S. Checcoli and F. Veneziano we investigated the Torsion Anomalous Conjecture, that studies conditions under which certain intersections are dense or not. This conjecture received a lot of attention over several years and it is well known to imply the Mordell-Lang Conjecture. To prove it in general remains an open question. I will present the known results and in particular I would like to present our effective method to prove it for transverse curves. This allow us to imply new cases of the explicit Mordell-Conjecture. We were successful in finding the rational points on some new families of curves of growing genus, given the equations of the curves we list the rational points. The previous explicit examples are families of curves of genus 2 or 3 and few curves of genus at most 10. I will explain our method, its limit and generalisations.