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Author Clark, Pete L
Title Rational points on Atkin-Lehner quotients of Shimura curves
book jacket
Descript 184 p
Note Source: Dissertation Abstracts International, Volume: 64-05, Section: B, page: 2214
Adviser: Barry Mazur
Thesis (Ph.D.)--Harvard University, 2003
We study three families of Atkin-Lehner 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 64-05B
Subject Mathematics
0405
Alt Author Harvard University
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