Title: p-adic equidistribution of CM points on modular curves
Abstract: Let X be a modular curve. It is a curve over the integers, whose complex points form a quotient of the upper half-plane by a subgroup of SL(2,Z). In X there is a natural supply of algebraic points called CM points. After an idea of Heegner, they can be used to construct rational points on elliptic curves.
How are CM points distributed "in X"? Let z_n be a sequence of CM points of increasing p-conductor for some prime p. Various works from the 2000s show that (the images of) the z_n equidistribute to natural measures on X(C) and on X(F_q) for suitable primes q different from p.
I will talk about an equidistribution result for the z_n in the p-adic analytic curve attached to X, and its application to the study of Heegner points.