Jayce Getz, U Wisconsin, Madison

"Hilbert modular generating functions with coefficients in
intersection homology"

(joint work with M. Goresky)

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
fields.