University of Sydney Algebra Seminar

Cristian Virdol

Friday 19th August, 12.05-12.55pm, Carslaw 275

Tate classes and L-functions of twisted quaternionic Shimura surfaces

We consider some twisted quaternionic Shimura surfaces obtained from the quaternionic Shimura surface S_\Gamma(N) asociated to the principal congruence subgroup \Gamma(N) via twisting by a representation of the absolute Galois group of the field of definition of S_\Gamma(N). We will prove that the order of the pole at s=2 of the zeta function of twisted quaternionic Shimura surfaces is equal to the dimension of the Tate cycles of these surfaces. This fact is a generalization of some results obtained by Langlands, Rapoport and Harder in the case of Hilbert modular surfaces.