Diophantine properties of Atkin -Lehner quotients of Shimura curves.

Title: Diophantine properties of Atkin -Lehner quotients of Shimura curves.
Identifier: AAI9946135
identifier: 9946135
Creator: Baba, Srinath.
Contributor: Adviser: Bruce Jordan
Date: 1999
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Let VB be the Shimura curve attached to an indefinite rational quaternion algebra B of odd discriminant D, and W be the group of Atkin-Lehner involutions acting on it. In this thesis, we study the Diophantine properties of quotients VB/G, where G is any subgroup of W.;We analyse the existence of rational points over local fields. Using the results obtained, we study the existence of divisors and divisor classes of degree d over local fields. Using this information, we analyse the Cassels-Tate pairing on III(A/ Q), where A = Pic0(V B/G), and conclude exactly when it is alternating and when it fails to be alternating, using the criteria of Poonen and Stoll.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.