Naina Praveen

What can torsion tell us about reduction types?

Reducing an elliptic curve modulo a prime can introduce singularities, whose structure is classified by the Kodaira type. From the perspective of Galois representations, the action on torsion points can be used to detect good reduction, but it does not always determine the Kodaira type. In this talk, I will explain how incorporating the p-adic distances between the x-coordinates of torsion points provides additional information that can recover the Kodaira type. I will illustrate these ideas with examples and briefly discuss the additional subtleties that arise at p=2 and 3.