The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
The University of Sydney USyd Home  MyUni MyUni  Library  Sitemap 
 About the School 
 Research Activities 
 For prospective students 
 For current students 
 School Internal Web Site 

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.