Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
scheme |
| gptkbp:basisFor |
gptkb:Zariski_topology
|
| gptkbp:category |
opposite category of commutative rings
|
| gptkbp:definedIn |
locally ringed space isomorphic to Spec(R) for some commutative ring R
|
| gptkbp:example |
gptkb:Spec(k[x])
gptkb:Spec(Z) |
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:generalizes |
gptkb:affine_varieties
|
| https://www.w3.org/2000/01/rdf-schema#label |
affine schemes
|
| gptkbp:introduced |
gptkb:Alexander_Grothendieck
|
| gptkbp:morphism |
corresponds to ring homomorphism in opposite direction
|
| gptkbp:property |
every scheme is locally an affine scheme
|
| gptkbp:relatedTo |
commutative rings
Spec functor |
| gptkbp:structureSheaf |
sheaf of rings on Spec(R)
|
| gptkbp:subclassOf |
schemes
|
| gptkbp:usedIn |
modern algebraic geometry
|
| gptkbp:bfsParent |
gptkb:Tate's_acyclicity_theorem
|
| gptkbp:bfsLayer |
6
|