Localization in lower algebraic k-theory

DOI10.1080/00927878008822478zbMath0429.16019OpenAlexW2000549181MaRDI QIDQ3866233

David W. Carter

Publication date: 1980

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927878008822478

zbMATH Keywords

finitely generated moduleslocalization sequencefinite resolutionlower K-theorylower K-groups

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Grothendieck groups, (K)-theory, etc. (16E20) Group rings (16S34) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Localization and associative Noetherian rings (16P50) Grothendieck groups, (K)-theory and commutative rings (13D15)

Related Items (22)

The groups \(N^ rK_ 0(\mathbb{Z}\pi )\) are finitely generated \(\mathbb{Z} [\mathbb{N}^ r\)-modules if \(\pi\) is a finite group] ⋮ The lower algebraic \(K\)-theory of virtually infinite cyclic groups ⋮ Bounded Homotopy Equivalences of Hilbert Cube Manifolds ⋮ \(K_{-i}\) obstructions to factoring an open manifold ⋮ Automorphisms of manifolds and algebraic K-theory. I ⋮ K-theory and analytic isomorphisms ⋮ The integral Novikov conjectures for linear groups containing torsion elements ⋮ Lower K-theory of nilpotent groups ⋮ A Brown-Gersten spectral sequence for the K-theory of varieties with isolated singularities ⋮ Semifree topological actions of finite groups of spheres ⋮ On the ranks of the algebraic \(K\)-theory of hyperbolic groups ⋮ Higher algebraic \(K\)-theory of admissible abelian categories and localization theorems ⋮ Higher algebraic \(K\)-theory for twisted Laurent series rings over orders and semisimple algebras ⋮ Twisting L2-invariants with finite-dimensional representations ⋮ Relative Cartier divisors and Laurent polynomial extensions ⋮ Negative \(K\)-theory of derived categories ⋮ Algebraic K-theory ⋮ The lower algebraic \(K\)-theory of \(\Gamma_{3}\) ⋮ Lower k-theory of finite groups ⋮ On the relative \(K\)-group in the ETNC. III ⋮ Negative K-Theory of Generalized Quaternion Groups and Binary Polyhedral Groups ⋮ Negative K-theory of varieties with isolated singularities

Cites Work

• The functors \(K_{-i}\) and pseudo-isotopies of polyhedra
• Higher algebraic K-theory: I
• The localization theorem for protective modules

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