Statements (96)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:appliesTo |
categories
rings schemes |
| gptkbp:field |
gptkb:algebraic_K-theory
|
| gptkbp:generalizes |
gptkb:Grothendieck_group
|
| https://www.w3.org/2000/01/rdf-schema#label |
higher algebraic K-theory
|
| gptkbp:introduced |
gptkb:Daniel_Quillen
|
| gptkbp:introducedIn |
1972
|
| gptkbp:notableAchievement |
gptkb:K-theory_of_C*-algebras
gptkb:K-theory_of_operator_algebras gptkb:Milnor_K-theory gptkb:Farrell–Jones_conjecture gptkb:Beilinson–Lichtenbaum_conjecture gptkb:Quillen's_Q-construction gptkb:Quillen–Lichtenbaum_conjecture gptkb:Waldhausen_S-construction gptkb:Bloch–Lichtenbaum_spectral_sequence gptkb:Bass'_Fundamental_Theorem gptkb:Devissage_Theorem gptkb:Fundamental_Theorem_of_Algebraic_K-theory gptkb:K-theory_of_algebraic_varieties gptkb:K-theory_of_dg-categories gptkb:K-theory_of_finite_fields gptkb:K-theory_of_motives gptkb:K-theory_of_topological_spaces K-theory of schemes plus construction K-theory of fields K-theory of triangulated categories K-theory of Azumaya algebras K-theory of Banach algebras K-theory of Eilenberg–MacLane spaces K-theory of Grassmannians K-theory of Hopf algebras K-theory of Lie algebras K-theory of algebraic cycles K-theory of algebraic groups K-theory of algebraic stacks K-theory of braided categories K-theory of central simple algebras K-theory of chain complexes K-theory of classifying spaces K-theory of coherent sheaves K-theory of complexes K-theory of derived algebraic geometry K-theory of derived categories K-theory of division algebras K-theory of elliptic curves K-theory of exact categories K-theory of exact functors K-theory of flag varieties K-theory of fusion categories K-theory of global fields K-theory of group rings K-theory of infinity categories K-theory of local fields K-theory of model categories K-theory of modular forms K-theory of modules K-theory of monoidal categories K-theory of motivic homotopy theory K-theory of noncommutative geometry K-theory of number fields K-theory of presheaves K-theory of projective spaces K-theory of quadratic forms K-theory of ring spectra K-theory of ringed spaces K-theory of sheaves K-theory of simplicial objects K-theory of singularities K-theory of spectra K-theory of stable categories K-theory of stable homotopy theory K-theory of stacks K-theory of symmetric monoidal categories K-theory of symmetric spaces K-theory of tensor categories K-theory of topoi K-theory of topological algebras K-theory of toric varieties K-theory of vector bundles K-theory of von Neumann algebras Localization Theorem Resolution Theorem |
| gptkbp:relatedTo |
gptkb:algebraic_geometry
gptkb:topology number theory motivic cohomology |
| gptkbp:studies |
K-groups for n > 0
|
| gptkbp:uses |
homotopy theory
Waldhausen categories exact categories |
| gptkbp:bfsParent |
gptkb:Motivic_K-theory
|
| gptkbp:bfsLayer |
6
|