scholarly journals Tate classes and poles of L-functions of twisted quaternionic Shimura surfaces

2007 ◽  
Vol 123 (2) ◽  
pp. 315-328 ◽  
Author(s):  
Cristian Virdol
Keyword(s):  
Shimura Surfaces

scholarly journals Intersection theory on Shimura surfaces II

2010 ◽  
Vol 183 (1) ◽  
pp. 1-77 ◽  
Author(s):  
Benjamin Howard
Keyword(s):  
Intersection Theory ◽  
Shimura Surfaces

scholarly journals Intersection theory on Shimura surfaces

2009 ◽  
Vol 145 (2) ◽  
pp. 423-475 ◽  
Author(s):  
Benjamin Howard
Keyword(s):  
Fourier Coefficients ◽  
Complex Multiplication ◽  
Intersection Theory ◽  
Integral Model ◽  
Shimura Curve ◽  
Codimension One ◽  
Integral Weight ◽  
Intersection Multiplicities ◽  
General Program ◽  
Shimura Surfaces

AbstractKudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, in which one intersects two codimension one cycles on the integral model of a Shimura curve, has been completed by Kudla, Rapoport and Yang. In the present paper we prove results in a higher dimensional setting. On the integral model of a Shimura surface we consider the intersection of a Shimura curve with a codimension two cycle of complex multiplication points, and relate the intersection to certain cycle classes constructed by Kudla, Rapoport and Yang. As a corollary we deduce that our intersection multiplicities appear as Fourier coefficients of a Hilbert modular form of half-integral weight.

scholarly journals Plurigenera of general type surfaces in mixed characteristic

2008 ◽  
Vol 144 (5) ◽  
pp. 1214-1226 ◽  
Author(s):  
Junecue Suh
Keyword(s):  
General Type ◽  
Geometric Genus ◽  
Mixed Characteristic ◽  
Reduction Modulo ◽  
Shimura Surfaces

AbstractWe construct general type surfaces in mixed characteristic whose geometric genera can be made to jump by an arbitrarily prescribed positive amount under specialization. We then show that this phenomenon of jumping geometric genus presents itself in some compact Shimura surfaces. Finally, we find a set of conditions, met by the latter Shimura surfaces, that forces the higher plurigenera to remain constant in reduction modulo p.

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