Page 1 The K-book An Introduction to Algebraic K-theory Charles A. Weibel Graduate Studies
in Mathematics Volume 145 American Mathematical Society Page 2 The K-book An Introduction …

Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

The original goal that ultimately led to this volume was the construction of" motivic
cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum …

Beginning with the Bloch–Lichtenbaum exact couple relating the motivic cohomology of a
field F to the algebraic K-theory of F, the authors construct a spectral sequence for any …

We establish a general “affine representability” result in A 1-homotopy theory over a general
base. We apply this result to obtain representability results for vector bundles in A 1 …

A new approach to stable motivic homotopy theory is given. It is based on Voevodsky's
theory of framed correspondences. Using the theory, framed motives of algebraic varieties …

We examine some of the basic properties satisfied by Bloch's cycle complexes for quasi-
projective varieties over a field, and extend some of them to the cycle complex of a scheme …

The main purpose of these notes is to show that Grayson's motivic cohomology coincides
with the usual definition of motivic cohomology-see [V2, SV] for example and hence …

We describe a simple construction of the spectral sequence relating algebraic K-theory and
motivic cohomology modulo two general conjectures on the structure of the motivic …

Using the theory of framed correspondences developed by Voevodsky, we introduce and
study framed motives of algebraic varieties. They are the major computational tool for …