The purpose of this paper is to define Chern classes for higher algebraic K-theory in the
greatest possible generality and to generalize the Riemann-Roch theorems of Grothendieck …

0.1. The best known among the various definitions of algebraic K-theory is due to D. Quillen.
Recall his construction. Let A be a ring and GL (AI be the group of infinite invertible matrices …

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 …

In this paper we prove a localization theorem for the K-theory of commutative rings and of
schemes, Theorem 7.4, relating the K-groups of a scheme, of an open subscheme, and of …

We develop a theory of module categories over monoidal categories (this is a
straightforward categorization of modules over rings). As applications we show that any …

Page 1 WINFRIED BRUNS JOSEPH GUBELADZE Polytopes, Rings, and K-Theory Springer
Springer Monographs in Mathematics Page 2 Springer Monographs in Mathematics For further …

Chow Groups with Coefficients Page 1 Doc. Math. J. DMV 319 Chow Groups with Coefficients
Markus Rost Received: October 18, 1996 Communicated by Alexander S. Merkurjev Abstract …

In (13), Quillen defines a higher algebraic K-theory by taking homotopy groups of the
classifying spaces of certain categories. Certain questions in K-theory then become …

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the
algebraic K-and L-theory of integral group rings and to the Baum–Connes Conjecture on the …

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