08-12-2026, 12:57 PM
Quaternion Algebras
BY [John Voight]
Summary
Quaternion Algebras by John Voight is a comprehensive, open-access graduate-level textbook that develops the theory and arithmetic of quaternion algebras and their orders, connecting noncommutative algebra with quadratic forms, number theory, geometry, topology, and arithmetic geometry. The book begins with the algebraic foundations of quaternions and simple algebras, then studies integral structures, orders, ideals, local and global fields, discriminants, and zeta functions.
It subsequently explores applications to hyperbolic geometry and low-dimensional topology, before concluding with topics such as modular forms, supersingular elliptic curves, and abelian surfaces with quaternionic multiplication. With 43 chapters and numerous exercises, it serves both as an accessible introduction for graduate students and as a broad reference for researchers working in algebra, number theory, and arithmetic geometry.
BOOK [FREE AS A PDF]
BY [John Voight]
Summary
Quaternion Algebras by John Voight is a comprehensive, open-access graduate-level textbook that develops the theory and arithmetic of quaternion algebras and their orders, connecting noncommutative algebra with quadratic forms, number theory, geometry, topology, and arithmetic geometry. The book begins with the algebraic foundations of quaternions and simple algebras, then studies integral structures, orders, ideals, local and global fields, discriminants, and zeta functions.
It subsequently explores applications to hyperbolic geometry and low-dimensional topology, before concluding with topics such as modular forms, supersingular elliptic curves, and abelian surfaces with quaternionic multiplication. With 43 chapters and numerous exercises, it serves both as an accessible introduction for graduate students and as a broad reference for researchers working in algebra, number theory, and arithmetic geometry.
BOOK [FREE AS A PDF]
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