Descript 
184 p 
Note 
Source: Dissertation Abstracts International, Volume: 6405, Section: B, page: 2214 

Adviser: Barry Mazur 

Thesis (Ph.D.)Harvard University, 2003 

We study three families of AtkinLehner quotients of quaternionic Shimura curves: XD+, XD+0 (N), and XD+1 (N), which serve as moduli spaces of abelian surfaces with potential quaternionic multiplication (PQM) and level N structure. The arithmetic geometry of these curves is similar to, but even richer than, that of the classical modular curves. Two important differences are the existence of a nontrivial obstruction to an abelian surface being defined over its field of moduli and the lack of cusps, due to which there may fail to be any points rational over a given field. We study the existence of points on these curves rational over both local and global fields, and consider applications to the existence of PQM surfaces over Q 

School code: 0084 

DDC 
Host Item 
Dissertation Abstracts International 6405B

Subject 
Mathematics


0405

Alt Author 
Harvard University

