Doctor of Philosophy / The Hecke character of an abelian variety A/F is an isogeny invariant and the Galois action is such that A is isogenous to its Galois conjugate A^σ if and only if the corresponding Hecke character is fixed by σ. The quadratic twist of A by an extension L/F corresponds to multiplication of the associated Hecke characters. This leads us to investigate the Galois groups of families of quadratic extensions L/F with restricted ramification which are normal over a given subfield k of F. Our most detailed results are given for the case where k is the field of rational numbers and F is a field of definition for an elliptic curve with complex multiplication by K. In this case the groups which occur as Gal(L/K) are closely related to the 4-torsion of the class group of K. We analyze the structure of the local unit groups of quadratic fields to find conditions for the existence of curves with good reduction everywhere. After discussing the question of finding models for curves of a given Hecke character, we use twists by 3-torsion points to give an algorithm for constructing models of curves with known Hecke character and good reduction outside 3. The endomorphism algebra of the Weil restriction of an abelian variety A may be determined from the Grössencharacter of A. We describe the computation of these algebras and give examples in which A has dimension 1 or 2 and its Weil restriction has simple abelian subvarieties of dimension ranging between 2 and 24.

Thesis (Ph. D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 58-06, Section: B, page: 3074. Adviser: V.P. Snaith.

Thesis (Ph.D.) - Carleton University, 2002. / Includes bibliographical references (p. 98-100). Also available in electronic format on the Internet.

Thesis (M.Ed. (Education)) - Rhodes University, 2008.

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (Ph.D.)--Washington State University. / Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1974. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis--Basel. / Bibliography: p. 184-189.

Thesis (M.S.)--Boise State University, 2009. / Title from t.p. of PDF file (viewed June 15, 2010). Includes abstract. Includes bibliographical references (leaf 82).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.