Arithmetic intersections of Heegner divisors on the non-split Cartan modular curveMPIM

by Elie Studnia (MPIM)

Wednesday Nov 11, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

In 1985, Gross and Zagier factor the norm of the algebraic integer j(s)-j(t), where s,t generate the rings of integers of two imaginary quadratic fields with coprime discriminants. From a bird's eye view, their proof amounts to computing the arithmetic intersection of certain CM divisors on the modular curve X(1). This joint work with Jan Vonk and Jonathan Love is one of many existing generalizations of Gross and Zagier's result. We determine the arithmetic intersection of analogous Heegner divisors on the modular curve Xns+(p), where p is prime. One of the new difficulties is that, unlike in Gross—Zagier, intersections may happen in the fibre at which the curve has bad reduction. We solve this by finding a new modular interpretation for this fibre.
* Please note that there is a possibility that the talk can be recorded: This will be confirmed later by the speaker.