Rational algebraic \(K\)-theory of topological \(K\)-theory

DOI10.2140/gt.2012.16.2037zbMath1260.19004arXiv0708.2160OpenAlexW3122635153MaRDI QIDQ691546

Christian Ausoni, John Rognes

Publication date: 3 December 2012

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.2160

zbMATH Keywords

determinantsalgebraic \(K\)-theoryrational homotopytopological \(K\)-theory2-vector bundlesbordism spectra

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Topological (K)-theory (55N15) Topological (K)-theory (19L99) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Higher algebraic (K)-theory (19D99)

Related Items

Descent in algebraic \(K\)-theory and a conjecture of Ausoni-Rognes, Rings and modules in Kan spectra, Higher topological Hochschild homology of periodic complex K-theory, Determinant map for the prestack of Tate objects, On the algebraic \(K\)-theory of the complex \(K\)-theory spectrum, The stable symplectic category and a conjecture of Kontsevich, Twisted iterated algebraic \(K\)-theory and topological T-duality for sphere bundles, On the \(K\)-theory of pullbacks, Redshift and multiplication for truncated Brown-Peterson spectra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Relative algebraic K-theory and cyclic homology
• Algebraic K-theory of spaces and the Novikov conjecture
• The localization sequence for the algebraic \(K\)-theory of topological \(K\) -theory
• On the algebraic \(K\)-theory of the complex \(K\)-theory spectrum
• \(E_\infty\) ring spaces and \(E_\infty\) ring spectra. With contributions by Frank Quinn, Nigel Ray, and Jorgen Tornehave
• On the \(p\)-typical curves in Quillen's \(K\)-theory
• Trace maps from the algebraic \(K\)-theory of the integers (after Marcel Bökstedt)
• Topological André--Quillen cohomology and \(E_{\infty}\) André--Quillen cohomology
• On the \(K\)-theory of local fields
• Algebraic \(K\)-theory of topological \(K\)-theory
• The cyclotomic trace and algebraic K-theory of spaces
• A model for computing rational algebraic K-theory of simply connected spaces
• Units of ring spectra and their traces in algebraic K-theory
• On the construction of the Kan loop group
• On the multiplicative structure of topological Hochschild homology
• Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere
• On the structure of Hopf algebras
• Model Categories of Diagram Spectra
• Stable bundles over rig categories
• Topological Hochschild homology of connective complex K -theory
• Stable real cohomology of arithmetic groups
• Stable homotopical algebra and Γ-spaces
• THE CYCLOTOMIC TRACE FOR S-ALGEBRAS
• Symmetric spectra
• Galois extensions of structured ring spectra. Stably dualizable groups
• Loop spaces, characteristic classes and geometric quantization