**Proceedings of Symposia in Pure Mathematics**

Volume: 58;
1995;
444 pp;
Hardcover

MSC: Primary 12; 14; 16; 19;

**Print ISBN: 978-0-8218-0340-0
Product Code: PSPUM/58.2**

List Price: $121.00

AMS Member Price: $96.80

MAA Member Price: $108.90

**Electronic ISBN: 978-0-8218-9361-6
Product Code: PSPUM/58.2.E**

List Price: $114.00

AMS Member Price: $91.20

MAA Member Price: $102.60

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# \(K\)-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras

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*Bill Jacob; Alex Rosenberg*

# Table of Contents

## $K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras

- Contents vii8
- Part 2 v6 free
- Preface xi12 free
- On the Witt ring of elliptic curves 114 free
- p-algebras over maximally complete fields 2740
- Weil's additive characters and class number parity 5164
- Decomposition of positive definite integral quadratic forms as sums of positive definite quadratic forms 6376
- Multiples of trace forms in number fields 7386
- On the structure of Galois groups of the fields of rational functions 8396
- Formal groups of twisted multiplicative groups and L-series 89102
- Sums of squares of real polynomials 103116
- Unramified Witt groups of real anisotropic quadrics 127140
- Orderings, valuations, and Hermitian forms over *-fields 149162
- A conjecture about relative Brauer groups 161174
- Bernstein's isomorphism and good forms 171184
- Examples of locally trivial Azumaya algebras 197210
- Isotropy of 5-dimensional quadratic forms over the function field of a quadric 217230
- Minimal forms for function fields of conies 227240
- Generalized class field theory and cyclic algebras 239252
- The number of embeddings of quadratic 5-lattices 265278
- On topological filtration for Severi-Brauer varieties 275288
- Discriminants of involutions on biquaternion algebras 279292
- p-groups and K-admissibility 305318
- Brauer groups over affine normal surfaces 309322
- Certain K-cohomology groups of Severi-Brauer varieties 319332
- The u-invariant for algebraic extensions 333346
- On defective division algebras 359372
- Products of Severi-Brauer varieties and Galois cohomology 369382
- A finiteness theorem for cohomology of surfaces over P-adic fields and an application to Witt groups 403416
- Witt rings and readability of small 2-Galois groups 417430
- Quadratic forms and solvable Galois groups 425438
- Symmetric and skew-symmetric elements of involutions, associated groups, and the problem of decomposability of involutions 431444