Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
smooth projective varieties
|
| gptkbp:category |
gptkb:mathematics
|
| gptkbp:describes |
relationship between cohomology groups
|
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:generalizes |
gptkb:Riemann–Roch_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Serre duality
|
| gptkbp:influenced |
gptkb:Grothendieck_duality
|
| gptkbp:introducedIn |
1955
|
| gptkbp:involves |
dualizing sheaf
sheaf cohomology |
| gptkbp:namedAfter |
gptkb:Jean-Pierre_Serre
|
| gptkbp:provides |
perfect pairing between cohomology groups
|
| gptkbp:relatedTo |
gptkb:Poincaré_duality
cohomology of a sheaf cohomology of the dualizing sheaf |
| gptkbp:sentence |
For a smooth projective variety X of dimension n over a field k, and a coherent sheaf F, there is a natural isomorphism H^i(X, F) ≅ H^{n-i}(X, ω_X ⊗ F^*)^*
|
| gptkbp:usedIn |
gptkb:topology
complex geometry |
| gptkbp:bfsParent |
gptkb:Jean-Pierre_Serre
|
| gptkbp:bfsLayer |
4
|