Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:appliesTo |
algebraic varieties
schemes |
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:topology |
| gptkbp:generalizes |
classical homotopy theory
|
| gptkbp:hasApplication |
gptkb:algebraic_K-theory
gptkb:Bloch–Kato_conjecture gptkb:Milnor_conjecture quadratic forms algebraic cycles enumerative geometry motivic stable homotopy groups |
| gptkbp:hasConcept |
gptkb:A1-homotopy_category
A1-weak equivalence |
| https://www.w3.org/2000/01/rdf-schema#label |
A1-homotopy theory
|
| gptkbp:influenced |
stable motivic homotopy theory
|
| gptkbp:introduced |
gptkb:Vladimir_Voevodsky
gptkb:Fabien_Morel |
| gptkbp:introducedIn |
late 1990s
|
| gptkbp:notableAchievement |
proof of Bloch–Kato conjecture
proof of Milnor conjecture |
| gptkbp:notableIdea |
gptkb:motivic_Steenrod_algebra
gptkb:motivic_sheaves gptkb:motivic_spectral_sequence gptkb:motivic_stable_homotopy_category gptkb:motivic_Adams_spectral_sequence motivic cohomology A1-contractibility A1-homotopy groups motivic Eilenberg–MacLane spaces motivic Hopf map motivic Postnikov tower motivic cobordism motivic infinite Grassmannians motivic infinite loop space machine motivic infinite loop spaces motivic infinite projective spaces motivic infinite symmetric products motivic localization motivic model structure motivic spheres motivic stable homotopy groups motivic stable stems |
| gptkbp:relatedTo |
gptkb:motivic_homotopy_theory
motivic cohomology |
| gptkbp:studies |
homotopy theory of schemes
|
| gptkbp:uses |
gptkb:étale_topology
gptkb:Nisnevich_topology simplicial sheaves |
| gptkbp:bfsParent |
gptkb:Algebraic_Homotopy
|
| gptkbp:bfsLayer |
6
|