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001431086 001__ 1431086
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001431086 019__ $$a1266811759
001431086 020__ $$a9783030566944$$q(electronic bk.)
001431086 020__ $$a3030566943$$q(electronic bk.)
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001431086 020__ $$z9783030566920
001431086 0247_ $$a10.1007/978-3-030-56694-4$$2doi
001431086 035__ $$aSP(OCoLC)1258658936
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001431086 1001_ $$aVoight, John,$$eauthor.
001431086 24510 $$aQuaternion algebras /$$cJohn Voight
001431086 264_1 $$aCham :$$bSpringer,$$c2021.
001431086 300__ $$a1 online resource
001431086 336__ $$atext$$btxt$$2rdacontent
001431086 337__ $$acomputer$$bc$$2rdamedia
001431086 338__ $$aonline resource$$bcr$$2rdacarrier
001431086 347__ $$atext file
001431086 347__ $$bPDF
001431086 4901_ $$aGraduate texts in mathematics,$$x0072-5285 ;$$v288
001431086 504__ $$aIncludes bibliographical references and index.
001431086 5050_ $$a1. Introduction -- 2. Beginnings -- 3. Involutions -- 4. Quadratic Forms -- 5. Ternary Quadratic Forms -- 6. Characteristic 2 -- 7. Simple Algebras -- 8. Simple Algebras and Involutions -- 9. Lattices and Integral Quadratic Forms -- 10. Orders -- 11. The Hurwitz Order -- 12. Ternary Quadratic Forms Over Local Fields -- 13. Quaternion Algebras Over Local Fields -- 14. Quaternion Algebras Over Global Fields -- 15. Discriminants -- 16. Quaternion Ideals and Invertability -- 17. Classes of Quaternion Ideals -- 18. Picard Group -- 19. Brandt Groupoids -- 20. Integral Representation Theory -- 21. Hereditary and Extremal Orders -- 22. Ternary Quadratic Forms -- 23. Quaternion Orders -- 24. Quaternion Orders: Second Meeting -- 25. The Eichler Mass Formula -- 26. Classical Zeta Functions -- 27. Adelic Framework -- 28. Strong Approximation -- 29. Idelic Zeta Functions -- 30. Optimal Embeddings -- 31. Selectivity -- 32. Unit Groups -- 33. Hyperbolic Plane -- 34. Discrete Group Actions -- 35. Classical Modular Group -- 36. Hyperbolic Space -- 37. Fundamental Domains -- 38. Quaternionic Arithmetic Groups -- 39. Volume Formula -- 40. Classical Modular Forms -- 41. Brandt Matrices -- 42. Supersingular Elliptic Curves -- 43. Abelian Surfaces with QM.
001431086 5060_ $$aOpen access.$$5GW5XE
001431086 520__ $$aThis 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.
001431086 650_0 $$aQuaternions.
001431086 650_0 $$aFunctions, Quaternion.
001431086 650_6 $$aQuaternions.
001431086 650_6 $$aFonctions quaternioniennes.
001431086 655_0 $$aElectronic books.
001431086 77608 $$iPrint version:$$aVoight, John.$$tQuaternion algebras.$$dCham : Springer, 2021$$z3030566927$$z9783030566920$$w(OCoLC)1176327287
001431086 830_0 $$aGraduate texts in mathematics ;$$v288.$$x0072-5285
001431086 852__ $$bebk
001431086 85640 $$3Springer Nature$$uhttps://link.springer.com/10.1007/978-3-030-56694-4$$zOnline Access$$91397441.2
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001431086 980__ $$aBIB
001431086 980__ $$aEBOOK
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