Introduction to Quadratic Forms Over Fields

T.Y. Lam (Autor)

Buch | Softcover

550 Seiten

2005
American Mathematical Society (Verlag)
978-1-4704-8017-2 (ISBN)

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A new version of the author's prize-winning Algebraic Theory of Quadratic Forms (Benjamin, 1973), this book gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic not two. Starting with few prerequisites besides linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, field theory, algebraic geometry, algebraic topology, and geometric topology.

T.Y. Lam, University of California, Berkeley, CA

Chapters
Chapter 1. Foundations
Chapter 2. Introduction to Witt rings
Chapter 3. Quaternion algebras and their norm forms
Chapter 4. The Brauer-Wall group
Chapter 5. Clifford algebras
Chapter 6. Local fields and global fields
Chapter 7. Quadratic forms under algebraic extensions
Chapter 8. Formally real fields, real-closed fields, and Pythagorean fields
Chapter 9. Quadratic forms under transcendental extensions
Chapter 10. Pfister forms and function fields
Chapter 11. Field invariants
Chapter 12. Special topics in quadratic forms
Chapter 13. Special topics on invariants

Erscheint lt. Verlag	1.3.2005
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-8017-4 / 1470480174
ISBN-13	978-1-4704-8017-2 / 9781470480172
Zustand	Neuware