Algebraic K-theory of rings

URI: https://gptkb.org/entity/Algebraic_K-theory_of_rings

GPTKB entity

Statements (58)

Predicate	Object
gptkbp:instanceOf	gptkb:logic
gptkbp:appliesTo	commutative rings schemes noncommutative rings
gptkbp:defines	gptkb:K_0_group gptkb:K_1_group gptkb:K_2_group
gptkbp:developedBy	gptkb:John_Milnor gptkb:Daniel_Quillen
gptkbp:field	gptkb:algebraic_K-theory
gptkbp:generalizes	gptkb:Grothendieck_group
gptkbp:hasApplication	gptkb:algebraic_geometry gptkb:topology number theory motivic cohomology
https://www.w3.org/2000/01/rdf-schema#label	Algebraic K-theory of rings
gptkbp:introduced	gptkb:Alexander_Grothendieck
gptkbp:notableAchievement	gptkb:Milnor_K-theory gptkb:Farrell–Jones_conjecture gptkb:Bass–Quillen_conjecture gptkb:Fundamental_theorem_of_algebraic_K-theory gptkb:Gersten_conjecture gptkb:Quillen's_Q-construction gptkb:Quillen–Lichtenbaum_conjecture gptkb:Bass'_fundamental_theorem gptkb:Bloch–Lichtenbaum_spectral_sequence gptkb:Devissage_theorem gptkb:Suslin_rigidity_theorem Localization theorem
gptkbp:relatedConcept	gptkb:Hermitian_K-theory gptkb:Whitehead_group gptkb:Karoubi–Villamayor_K-theory gptkb:Waldhausen_K-theory gptkb:higher_K-theory gptkb:Chow_groups gptkb:Mayer–Vietoris_sequence gptkb:motivic_homotopy_theory gptkb:Steinberg_group gptkb:SK_1_group gptkb:algebraic_K-theory_of_fields gptkb:algebraic_L-theory gptkb:algebraic_cobordism algebraic cycles motivic cohomology topological K-theory assembly map algebraic K-theory of schemes excision theorem
gptkbp:relatedTo	gptkb:algebraic_geometry gptkb:topology homological algebra
gptkbp:studies	gptkb:vector_bundles rings projective modules
gptkbp:uses	homotopy theory exact sequences
gptkbp:bfsParent	gptkb:K-theory
gptkbp:bfsLayer	5