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...
Saved in:
| Main Author: | |
|---|---|
| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2021.
|
| Edition: | 1st ed. 2021. |
| Series: | Graduate Texts in Mathematics,
288 |
| Subjects: | |
| Online Access: | Link to Metadata |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 1. Introduction
- 2. Beginnings
- 3. Involutions
- 4. Quadratic Forms
- 5. Ternary Quadratic Forms
- 6. Characteristic 2
- 7. Simple Algebras
- 8. Simple Algebras and Involutions
- 9. Lattices and Integral Quadratic Forms
- 10. Orders
- 11. The Hurwitz Order
- 12. Ternary Quadratic Forms Over Local Fields
- 13. Quaternion Algebras Over Local Fields
- 14. Quaternion Algebras Over Global Fields
- 15. Discriminants
- 16. Quaternion Ideals and Invertability
- 17. Classes of Quaternion Ideals
- 18. Picard Group
- 19. Brandt Groupoids
- 20. Integral Representation Theory
- 21. Hereditary and Extremal Orders
- 22. Ternary Quadratic Forms
- 23. Quaternion Orders
- 24. Quaternion Orders: Second Meeting
- 25. The Eichler Mass Formula
- 26. Classical Zeta Functions
- 27. Adelic Framework
- 28. Strong Approximation
- 29. Idelic Zeta Functions
- 30. Optimal Embeddings
- 31. Selectivity
- 32. Unit Groups
- 33. Hyperbolic Plane
- 34. Discrete Group Actions
- 35. Classical Modular Group
- 36. Hyperbolic Space
- 37. Fundamental Domains
- 38. Quaternionic Arithmetic Groups
- 39. Volume Formula
- 40. Classical Modular Forms
- 41. Brandt Matrices
- 42. Supersingular Elliptic Curves
- 43. Abelian Surfaces with QM.