Algebraic K-theory of schemes

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:logic
gptkbp:appliesTo	schemes
gptkbp:field	gptkb:algebraic_geometry gptkb:algebraic_K-theory
gptkbp:generalizes	gptkb:Grothendieck_group_of_vector_bundles
gptkbp:hasApplication	gptkb:topology gptkb:motivic_homotopy_theory number theory
gptkbp:hasConnection	gptkb:topology gptkb:Chow_groups gptkb:motivic_homotopy_theory algebraic number theory arithmetic geometry algebraic cycles motivic cohomology derived algebraic geometry topological K-theory algebraic stacks motivic spectral sequences
gptkbp:hasInvariant	gptkb:K_0 gptkb:K_1 gptkb:K_2 higher K-groups
https://www.w3.org/2000/01/rdf-schema#label	Algebraic K-theory of schemes
gptkbp:introduced	gptkb:Alexander_Grothendieck
gptkbp:notableAchievement	gptkb:Milnor_K-theory gptkb:Riemann–Roch_theorem gptkb:Bass–Quillen_conjecture gptkb:Gersten_conjecture gptkb:Bloch–Lichtenbaum_spectral_sequence gptkb:Devissage_theorem gptkb:Fundamental_theorem_of_K-theory gptkb:Quillen's_localization_theorem gptkb:Thomason–Trobaugh_descent_theorem
gptkbp:relatedTo	gptkb:higher_Chow_groups algebraic cycles motivic cohomology
gptkbp:studies	K-groups of schemes
gptkbp:uses	gptkb:Quillen's_Q-construction homotopy theory Waldhausen categories exact categories sheaf theory spectra cohomological methods derived categories exact sequences localization sequences
gptkbp:bfsParent	gptkb:K-theory
gptkbp:bfsLayer	5