**Contemporary Mathematics**

Volume: 344;
2004;
350 pp;
Softcover

MSC: Primary 11;

**Print ISBN: 978-0-8218-3441-1
Product Code: CONM/344**

List Price: $110.00

AMS Member Price: $88.00

MAA Member Price: $99.00

**Electronic ISBN: 978-0-8218-7934-4
Product Code: CONM/344.E**

List Price: $103.00

AMS Member Price: $82.40

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# Algebraic and Arithmetic Theory of Quadratic Forms

Share this page *Edited by *
*Ricardo Baeza; John S. Hsia; Bill Jacob; Alexander Prestel*

This proceedings volume contains papers presented at the International
Conference on the algebraic and arithmetic theory of quadratic forms held in
Talca (Chile).

The modern theory of quadratic forms has connections with a broad
spectrum of mathematical areas including number theory, geometry, and
K-theory. This volume contains survey and research articles covering
the range of connections among these topics.

The survey articles bring readers up-to-date on research and open
problems in representation theory of integral quadratic forms, the
algebraic theory of finite square class fields, and developments in
the theory of Witt groups of triangulated categories. The specialized
articles present important developments in both the algebraic and
arithmetic theory of quadratic forms, as well as connections to
geometry and K-theory.

The volume is suitable for graduate students and research mathematicians
interested in various aspects of the theory of quadratic forms.

#### Readership

Graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.

# Table of Contents

## Algebraic and Arithmetic Theory of Quadratic Forms

- Contents v6 free
- Preface vii8 free
- Conference participants ix10 free
- The Milnor sequence for WqF(x) in characteristic 2 when F is perfect 112 free
- Spinor norm for local skew-Hermitian forms 1930
- An introduction to triangular Witt groups and a survey of applications 3142
- Regularity properties of positive definite integral quadratic forms 5970
- Effective results on representations of quadratic forms 7384
- Quaternary quadratic forms and Hilbert modular surfaces 8596
- Real semigroups and abstract real spectra. I 99110
- The role of characteristic vectors in the neighbour lattice process 121132
- On representation by quadratic Fq[x]-lattices 129140
- Diagonal forms of degree p in characteristic p 135146
- 1. Introduction 135146
- 2. Basic results 138149
- 3. A representation theorem à la Cassels-Pfister 141152
- 4. The norm field, the norm degree, and quasi-Pfister forms 144155
- 5. Behaviour of p-forms under algebraic field extensions 148159
- 6. Similarity factors of p-forms and a "norm theorem" à la Knebusch 154165
- 7. The behaviour of p-forms under function field extensions of p-forms 159170
- 7.1 The definition of the function field of a p-form 159170
- 7.2 The algebraic closure of the base field inside the function field of a p-form 160171
- 7.3 p-splitting of a p-form over the function field of a p-form 161172
- 7.4 Isotropy of p-forms over function fields of p-forms 164175
- 7.5 Some remarks on height and splitting patterns of p-forms 168179
- 7.6 Some applications to quasi-Pfister neighbors 171182

- 8. The behaviour of differential forms under function field extensions of p-forms 175186

- Local densities and the representations of an integer by a definite quadratic form 185196
- Periodicity of Hermitian K-theory and Milnors K-groups 197208
- Third proof of second gap in dimensions of quadratic forms from In 207218
- Recent developments on universal forms 215226
- Special Siegel modular forms and singular series polynomials of quadratic forms 229240
- Quasi-hyperbolicity of totally singular quadratic forms 237248
- Witt kernels of triquadratic extensions 249260
- Anti-automorphisms of the second kind 257268
- Reduction modulo 2 and 3 of Euclidean lattices, II 265276
- The elementary type conjecture in quadratic form theory 275286
- 1. Quadratic form schemes 276287
- 2. Quaternionic mappings and Witt rings 277288
- 3. Elementary constructions 279290
- 4. Uniqueness results and counting 281292
- 5. The reduced case 282293
- 6. The case of small value sets 284295
- 7. The case of few quaternion algebras 285296
- 8. Quotients 286297
- 9. Morphisms and field extensions 287298
- 10. Connections to Galois theory 287298

- On Hilbert's theorem about ternary quartics 295306
- Representation by integral quadratic forms–a survey 303314
- Representations by spinor genera of ternary quadratic forms 323334
- A survey and a complement of fundamental Hermite constants 339350