Statements (99)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:cohomology_theory
|
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:algebraic_K-theory |
| gptkbp:firstDefined |
1990s
|
| gptkbp:generalizes |
gptkb:Chow_groups
|
| gptkbp:hasApplication |
gptkb:algebraic_K-theory
gptkb:motivic_homotopy_theory arithmetic geometry |
| gptkbp:hasGrading |
bigraded
|
| https://www.w3.org/2000/01/rdf-schema#label |
Motivic cohomology
|
| gptkbp:introduced |
gptkb:Andrei_Suslin
gptkb:Vladimir_Voevodsky |
| gptkbp:isCohomologyTheoryOn |
algebraic varieties
schemes |
| gptkbp:notation |
H^{p,q}(X, A)
|
| gptkbp:relatedTo |
gptkb:étale_cohomology
gptkb:Beilinson–Lichtenbaum_conjecture gptkb:Bloch's_higher_Chow_groups gptkb:Chow_groups gptkb:motivic_Eilenberg–MacLane_spectrum gptkb:motivic_Galois_group gptkb:motivic_L-functions gptkb:motivic_Steenrod_algebra gptkb:motivic_fundamental_group gptkb:motivic_integration gptkb:motivic_polylogarithm gptkb:motivic_sheaves gptkb:motivic_spectral_sequence gptkb:motivic_stable_homotopy_category gptkb:motivic_zeta_function algebraic cycles singular cohomology cycle class map motives motivic cohomology of Galois extensions motivic cohomology of Grassmannians motivic cohomology of Gysin sequence motivic cohomology of Nisnevich topology motivic cohomology of Zariski topology motivic cohomology of abelian varieties motivic cohomology of affine schemes motivic cohomology of algebraic groups motivic cohomology of base change motivic cohomology of base change formula motivic cohomology of cdh topology motivic cohomology of characteristic zero motivic cohomology of classifying spaces motivic cohomology of closed varieties motivic cohomology of complex varieties motivic cohomology of curves motivic cohomology of descent motivic cohomology of duality motivic cohomology of elliptic curves motivic cohomology of field extensions motivic cohomology of fields motivic cohomology of finite fields motivic cohomology of finite type schemes motivic cohomology of fppf topology motivic cohomology of fpqc topology motivic cohomology of function fields motivic cohomology of h topology motivic cohomology of infinite type schemes motivic cohomology of local fields motivic cohomology of localization motivic cohomology of long exact sequence motivic cohomology of mixed characteristic motivic cohomology of number fields motivic cohomology of open varieties motivic cohomology of positive characteristic motivic cohomology of projective spaces motivic cohomology of proper schemes motivic cohomology of purity motivic cohomology of quasi-projective schemes motivic cohomology of real varieties motivic cohomology of regular schemes motivic cohomology of schemes motivic cohomology of singular schemes motivic cohomology of singular varieties motivic cohomology of smooth schemes motivic cohomology of spectral sequence motivic cohomology of stacks motivic cohomology of surfaces motivic cohomology of toric varieties motivic cohomology of varieties motivic cohomology of étale topology motivic cohomology operations motivic cohomology with compact support motivic cohomology with finite coefficients motivic cohomology with integer coefficients motivic cohomology with mod n coefficients motivic cohomology with rational coefficients motivic cohomology with supports motivic complexes motivic nearby cycles regulator map |
| gptkbp:usedIn |
proof of the Bloch–Kato conjecture
proof of the Milnor conjecture |
| gptkbp:bfsParent |
gptkb:algebraic_geometry
|
| gptkbp:bfsLayer |
5
|