p-adic equidistribution of CM points and applications

Seminar: 
Algebra and Number Theory Seminar
Event time: 
Tuesday, September 10, 2019 - 4:15pm
Location: 
LOM 205
Speaker: 
Daniel Disegni
Speaker affiliation: 
Ben Gurion University
Event description: 

Abstract: Consider a sequence of CM points of increasing p-adic conductor on a modular curve X. What is its limiting distribution in any of the geometric incarnations of X? Works from the 2000s give the answer for the Riemann surface X(C), and for the reduction of X modulo primes different from p. I will describe the answer in the p-adic (Berkovich) analytic setting.

A weak generalisation of this result has an application to the p-adic Birch and Swinnerton-Dyer conjecture.