Journal ArticleDOI
Localization in lower algebraic k-theory
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This article is published in Communications in Algebra.The article was published on 1980-01-01. It has received 49 citations till now. The article focuses on the topics: Algebraic element & Algebraic cycle.read more
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Book ChapterDOI
Higher Algebraic K-Theory of Schemes and of Derived Categories
R. W. Thomason,Thomas Trobaugh +1 more
TL;DR: In this article, a localization theorem for the K-theory of commutative rings and of schemes is presented, relating the k-groups of a scheme, of an open subscheme, and of those perfect complexes on the scheme which are acyclic on the open scheme.
Posted Content
The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory
TL;DR: A survey of the meaning, status and applications of the Baum-Connes Conjecture about the topological K-theory of the reduced group C^*-algebra can be found in this article.
Journal ArticleDOI
Negative K -theory of derived categories
TL;DR: In this paper, negative K-groups are defined for exact categories and derived categories in the framework of Frobenius pairs, generalizing definitions of Bass, Karoubi, Carter, Pedersen-Weibel and Thomason.
Journal ArticleDOI
K-Theory and Analytic Isomorphisms.
TL;DR: The Karoubi sequence was first exploited by Vorst in his thesis as mentioned in this paper, and has been used in a number of applications, such as answering a question of Murthy and computing a complete computation of an affine curve over an algebraically closed field.
Journal ArticleDOI
Delooping the K-theory of exact categories
TL;DR: In this paper, the concept of Karoubi filtration and the associated homotopy fibration in algebraic K-theory was generalized from additive categories to exact categories, and the following exact categories were constructed:
References
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Book
Linear Representations of Finite Groups
TL;DR: Representations and characters: generalities on linear representations character theory subgroups, products, induced representation compact groups examples.
Book
Introduction to algebraic K-theory
TL;DR: In this paper, the authors define an analogous functor K2 from associative rings to abelian groups, which has similar topological applications as K0 and K1, and show that K2 has similar properties as K-theory.