**Contemporary Mathematics**

Volume: 493;
2009;
408 pp;
Softcover

MSC: Primary 11; 12; 14; 19; 20;

Print ISBN: 978-0-8218-4648-3

Product Code: CONM/493

List Price: $115.00

Individual Member Price: $92.00

**Electronic ISBN: 978-0-8218-8172-9
Product Code: CONM/493.E**

List Price: $115.00

Individual Member Price: $92.00

# Quadratic Forms—Algebra, Arithmetic, and Geometry

Share this page *Edited by *
*Ricardo Baeza; Wai Kiu Chan; Detlev W. Hoffmann; Rainer Schulze-Pillot*

This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007.

The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.

#### Table of Contents

# Table of Contents

## Quadratic Forms -- Algebra, Arithmetic, and Geometry

- Contents vii8 free
- Preface ix10 free
- List of Participants xi12 free
- H1(X, ν) of conics and Witt kernels in characteristic 2 114 free
- Pythagoras numbers and quadratic field extensions 2134
- On perfection relations in lattices 2942
- Linear independence of local densities of quadratic forms and its application to the theory of Siegel modular forms 5164
- Representation of reduced special groups in algebras of continous functions 8396
- Solubility of Fermat equations 99112
- Multiplicative properties of integral binary quadratic forms 107120
- Effective structure theorems for symplectic spaces via height 117130
- Orthogonal involutions on algebras of degree 16 and the Killing form of E8 (with an appendix by Kirill Zainoulline) 131144
- The first Zariski cohomology group of the Witt sheaf over a split simply connected simple algebraic group 163176
- On families of testing formulae for a pp formula 181194
- Siegel modular forms of small weight and the Witt operator 189202
- On isotropy of quadratic pairs 211224
- Specialization of forms in the presence of characteristic 2: first steps 219232
- Representation of integers by special positive definite integral quadratic forms 243256
- Hyper-isotropy of bilinear forms in characteristic 2 249262
- A historical view of the Pythagoras numbers of fields 271284
- The extensions of R-places and application 289302
- Essential dimension 299312
- On the Pfister number of quadratic forms 327340
- Martin Kneser’s work on quadratic forms and algebraic groups 339352
- Enumerating perfect forms 359372
- Reduction mod l of Theta Series of Level ln 379392
- On a reciprocity theorem of Gauss 391404
- A bound of the number of reduced Arakelov divisors of a number field 399412

#### Readership

Graduate students and research mathematicians interested in quadradic forms (and their applications in algebra), number theory, and algebraic geometry.