HIRZEBRUCH–ZAGIER CYCLES IN p -ADIC FAMILIES AND ADJOINT L -VALUES

Let E / F $E/F$ upper E divided by upper F be a quadratic extension of totally real number fields. We show that the generalized Hirzebruch–Zagier cycles arising from the associated Hilbert modular varieties can be put in p -adic families. As an application, using the theory of base change, we give a geometric construction of the multivariable p -adic adjoint L -function twisted by the Hecke character of E / F $E/F$ upper E divided by upper F , attached to Hida families of Hilbert modular forms over F .