This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing seventeen survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A, D, E classification, centered around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric...

22. K-theory 230 A. Topological X-theory 230 Vector bundles and the functor Vec(X). Periodicity and the functors KJX). K(X) and t the infinite-dimensional linear group. The symbol of an elliptic differential operator. The index theorem. B. Algebraic K-theory 234 The group of classes of projective modules. K, K and K of a ring. K of a field and o l n 2 its relations with the Brauer group. K-theory and arithmetic. Comments on the Literature 239 References 244 Index of Names 249 Subject Index 251 Preface This book aims to present a general survey of algebra, of its basic notions and main...