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 …

The central organizational theorem of simplicial homotopy theory asserts that the category S
of simplicial sets has a closed model structure. This means that S comes equipped with …

Singular homology of abstract algebraic varieties. Contents Page 1 Singular homology of
abstract algebraic varieties. Andrei Suslin,Vladimir Voevodsky1 Contents 1 Introduction …

K3 of a field, and the Bloch group Page 235 Труды Матем. Инст. Стеклов. Proceedings of the
Steklov 183 (1990) Institute of Mathematics 1991, Issue 4 K, OF A FIELD AND THE BLOCH …

Let X be a noetherian scheme of finite Krull dimension. A new Grothendieck topology on X.
called the completely decomposed topology. is introduced, and the formalism of the …

This monograph on the homotopy theory of topologized diagrams of spaces and spectra
gives an expert account of a subject at the foundation of motivic homotopy theory and the …

Let $ S $ be a Noetherian scheme of finite dimension and denote by $\unicode
[STIX]{x1D70C}\in [\unicode [STIX]{x1D7D9},\mathbb {G} _ {m}] _ {\mathbf {SH}(S)} $ the …

Given a henselian pair $(R, I) $ of commutative rings, we show that the relative $ K $-theory
and relative topological cyclic homology with finite coefficients are identified via the …

A generalized etale cohomology theory is a theory which is represented by a presheaf of
spectra on an etale site for an algebraic variety, in analogy with the way an ordinary …

The present work continues earlier investigations by DuPont, Parry and this writer. One of
our motivating problems is the Scissors Congruence Problem (or Extended Third Problem of …