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gptkbp:instanceOf
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gptkb:logic
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gptkbp:appliesTo
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fields in mathematics
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gptkbp:concerns
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K_0, K_1, K_2, ... groups of fields
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gptkbp:field
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gptkb:algebraic_K-theory
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https://www.w3.org/2000/01/rdf-schema#label
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Algebraic K-theory of fields
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gptkbp:K_0
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isomorphic to Z for fields
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gptkbp:K_1
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isomorphic to multiplicative group of the field
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gptkbp:K_2
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described by Milnor K-theory
related to Steinberg group
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gptkbp:K_2_of_finite_field
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trivial
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gptkbp:K_2_of_local_field
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related to symbols in class field theory
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gptkbp:K_2_of_number_field
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related to class field theory
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gptkbp:K_3_of_field
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less understood
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gptkbp:K_n
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defined for all n ≥ 0
important in arithmetic geometry
related to Galois cohomology
related to motivic cohomology
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gptkbp:K_n_of_algebraically_closed_field
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known for small n
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gptkbp:K_n_of_complex_numbers
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related to topological K-theory
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gptkbp:K_n_of_finite_field
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periodic for n > 0
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gptkbp:K_n_of_real_numbers
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related to Bott periodicity
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gptkbp:K-theory_spectrum
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constructed by Quillen
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gptkbp:notableAchievement
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gptkb:Bloch-Kato_conjecture
gptkb:Merkurjev–Suslin_theorem
Quillen's computation of K-groups of finite fields
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gptkbp:notablePerson
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gptkb:John_Milnor
gptkb:Andrei_Suslin
gptkb:Alexander_Merkurjev
gptkb:Daniel_Quillen
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gptkbp:relatedTo
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gptkb:Milnor_K-theory
gptkb:motivic_homotopy_theory
gptkb:Beilinson_conjectures
gptkb:Bloch_group
gptkb:Lichtenbaum–Quillen_conjecture
gptkb:Quillen_K-theory
gptkb:higher_Chow_groups
algebraic cycles
Galois descent in K-theory
K-theory of rings
K-theory of schemes
Voevodsky's work on motivic cohomology
regulators in arithmetic geometry
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gptkbp:studies
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K-groups of fields
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gptkbp:usedIn
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gptkb:algebraic_geometry
number theory
motivic cohomology
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gptkbp:bfsParent
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gptkb:K-theory
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gptkbp:bfsLayer
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5
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