Higher algebraic \(K\)-theory of admissible abelian categories and localization theorems

DOI10.1016/0022-4049(92)90142-3zbMath0746.19006OpenAlexW2025603439MaRDI QIDQ1183353

Dongyuan Yao

Publication date: 28 June 1992

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(92)90142-3

zbMATH Keywords

excisionnoncommutative algebrasmooth varietyquasi-coherent sheavesleft modulesabelian categories with additional structureBass fundamental theoremlocalisation theoremsMayer- Vietorisprojective line bundle theoremsheaf of germs of differential operators

Mathematics Subject Classification ID

Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Higher algebraic (K)-theory (19D99) Localization of categories, calculus of fractions (18E35)

Related Items (11)

The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel ⋮ Reducing homological conjectures by \(n\)-recollements ⋮ \(K\)-theory of endomorphism rings and of rings of invariants ⋮ Noncommutative localisation in algebraic \(K\)-theory. I ⋮ On equivalence of derived categories ⋮ Invariance and localization for cyclic homology of DG algebras ⋮ A variant of the Mukai pairing via deformation quantization ⋮ Stratifying derived module categories ⋮ Negative \(K\)-theory of derived categories ⋮ On the cyclic homology of exact categories ⋮ Lifting of recollements and gluing of partial silting sets

Cites Work

• Localization for flat modules in algebraic K-theory
• K-theory and analytic isomorphisms
• K-theory and localization of noncommutative rings
• Riemann-Roch theorems for higher algebraic K-theory
• The K-theory of hereditary categories
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Algebraic $K$-theory and etale cohomology
• Localization in lower algebraic k-theory
• Higher algebraic K-theory: I
• The localization theorem for protective modules
• Algebraic \(K\)-theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Higher algebraic \(K\)-theory of admissible abelian categories and localization theorems