C o n t e n t s

PART 1

Preface

Birational invariants, purity, and the Gersten conjecture

J.-L. COLLIOT-THELfeNE 1

A'-theory of simple algebras

A. S. MERKURJEV 65

Abelian class field theory of arithmetic schemes

WAYNE RASKIND 85

Brauer groups of invariant fields, geometrically negligible classes, an

equivariant Chow group, and unramified

H3

DAVID J. SALTMAN 189

Higher algebraic ^-theory

RICHARD G. SWAN 247

PART 2

Preface

On the Witt ring of elliptic curves

JO N KR . ARASON, RICHARD ELMAN, AND BILL JACOB 1

p-algebras over maximally complete fields (with an Appendix by

J.-P. Tignol)

ROBERTO ARAVIRE AND BILL JACOB 27

Weil's additive characters and class number parity

STELLA ROBERSON ASHFORD 51

Decomposition of positive definite integral quadratic forms as sums of

positive definite quadratic forms

R. BAEZA AND M. I. ICAZA 63