Quaternion orders, quadratic forms, and Shimura curves / Montserrat Alsina, Pilar Bayer.

Format:

Book

Author/Creator:

Alsina, Montserrat, 1966- author.

Bayer i Isant, Pilar, author.

Series:

CRM monograph series ; Volume 22.

CRM Monograph Series ; Volume 22

Language:

English

Subjects (All):

Quaternions.

Forms, Quadratic.

Shimura varieties.

Physical Description:

1 online resource (199 pages) : illustrations, tables.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2004.

Summary:

Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. This monograph presents Shimura curves from a theoretical and algorithmic perspective. The main topics are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplicationpoints. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities that parallels Gauss'theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. This is one of the few available books explaining the theory of Shimura curves at the graduate student level. Each topic covered in the book begins with a theoretical discussion followed by carefully worked-out examples, preparing the way for further research.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1769-3