Hilbert Modular Generating Series with Coefficients in Intersection Homology

JOINT IAS/PU NUMBER THEORY
Topic:Hilbert Modular Generating Series with Coefficients in Intersection Homology
Speaker:J. Getz
Affiliation:Princeton University
Date:Thursday, September 27
Time/Room:4:30pm - 5:30pm/Fine Hall 214, Princeton University

In a seminal Inventiones 1976 paper, Hirzebruch and Zagier produced a set of cycles on certain Hilbert modular surfaces whose intersection numbers are the Fourier coefficients of elliptic modular forms with nebentypus. Their result can be viewed as a geometric manifestation of the Naganuma lift from elliptic modular forms to Hilbert modular forms. We discuss a general analogue of this result where the real quadratic extension is replaced by an arbitrary quadratic extension of totally real fields. Our result can be viewed as a geometric manifestation of quadratic base change for GL_2 over totally real