Quaternion algebras
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results f...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer
2021.
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| Colección: | Springer open access eBooks.
Graduate texts in mathematics; 288. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b46421610*spi |
| Sumario: | This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. |
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| Descripción Física: | 1 recurso electrónico |
| Formato: | Forma de acceso: World Wide Web. |
| Bibliografía: | Incluye referencias bibliográficas e índice. |
| ISBN: | 9783030566944 |
