Localization for flat modules in algebraic K-theory

DOI10.1016/0021-8693(79)90290-4zbMath0436.18010OpenAlexW2029121515MaRDI QIDQ1140709

Daniel R. Grayson

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0021-8693(79)90290-4

zbMATH Keywords

K-theoryalgebraic cycleslocalization theoremalgebraic K-theorySerre subcategoryrational equivalencelocalization for flat modules

Mathematics Subject Classification ID

Abelian categories, Grothendieck categories (18E10) (Equivariant) Chow groups and rings; motives (14C15) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35) Localization of categories, calculus of fractions (18E35)

Related Items (15)

The cyclic homology of an exact category ⋮ The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel ⋮ The localization sequence in \(K\)-theory ⋮ Algebraic 𝐾-theory via binary complexes ⋮ K-theory and localization of noncommutative rings ⋮ \(K_ 2 \)and \(K_ 3 \)of the circle ⋮ Arithmetic intersection theory ⋮ Higher algebraic \(K\)-theory of admissible abelian categories and localization theorems ⋮ The ``fundamental theorem for the higher algebraic \(K\)-theory of strongly \(\mathbb{Z}\)-graded rings ⋮ An algebraic proof of the commutativity of intersection with divisors ⋮ K₁ of Exact Categories by Mirror Image Sequences ⋮ Algebraic K-theory ⋮ Connecting homomorphisms in localization sequences. II ⋮ Grothendieck groups of polynomial and Laurent polynomial rings ⋮ Degree four cohomological invariants for quadratic forms

Cites Work

• Algebraic cycles and algebraic K-theory
• The K-theory of hereditary categories
• Products in K-theory and intersecting algebraic cycles
• \(K_2\) and the \(K\)-theory of automorphisms
• Introduction to Grothendieck duality theory
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• Higher algebraic K-theory: I
• K₂of artinian Q-algebras, with application to algebraic cycles
• The localization theorem for protective modules
• Algebraic \(K\)-theory

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