Statements (69)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:basisFor |
Modern algebraic geometry
|
| gptkbp:developedBy |
gptkb:Alexander_Grothendieck
|
| gptkbp:enables |
Unification of algebraic geometry and number theory
Study of varieties over arbitrary commutative rings |
| gptkbp:field |
gptkb:Algebraic_geometry
|
| gptkbp:generalizes |
Classical algebraic geometry
|
| gptkbp:hasConcept |
gptkb:Scheme
Sheaf Ringed space |
| https://www.w3.org/2000/01/rdf-schema#label |
Scheme theory
|
| gptkbp:influenced |
gptkb:Motivic_cohomology
gptkb:Moduli_theory Modern number theory Arithmetic geometry Algebraic stacks |
| gptkbp:introducedIn |
1960s
|
| gptkbp:notableBook |
gptkb:Algebraic_Geometry_by_Robin_Hartshorne
gptkb:Introduction_to_Commutative_Algebra_by_Atiyah_and_Macdonald Algebraic Geometry: A First Course by Joe Harris Basic Algebraic Geometry by Igor Shafarevich Algebraic Geometry and Arithmetic Curves by Qing Liu Éléments de géométrie algébrique by Grothendieck and Dieudonné The Red Book of Varieties and Schemes by David Mumford |
| gptkbp:notableIdea |
gptkb:Zariski_topology
gptkb:Sheaf_cohomology gptkb:Étale_morphism gptkb:Descent_theory Grothendieck topology Functoriality Universal property Noetherian scheme Projective scheme Spec of a ring Cohomology of schemes Affine scheme Base change Closed subscheme Fiber product of schemes Flatness Functor of points Generic point Irreducible scheme Morphisms of schemes Nilpotent element Open subscheme Proper morphism Quasi-coherent sheaf Reduced scheme Separated scheme Spectrum of a ring Structure sheaf |
| gptkbp:notablePerson |
gptkb:Jean-Pierre_Serre
gptkb:Michael_Artin gptkb:Robin_Hartshorne gptkb:David_Mumford gptkb:Pierre_Deligne gptkb:James_S._Milne gptkb:Shigeru_Mukai |
| gptkbp:publishedIn |
gptkb:Séminaire_de_Géométrie_Algébrique_du_Bois_Marie
gptkb:Éléments_de_géométrie_algébrique |
| gptkbp:relatedTo |
gptkb:Topology
gptkb:Commutative_algebra Category theory Homological algebra |
| gptkbp:bfsParent |
gptkb:Étale_morphism
gptkb:Etale_topology gptkb:Patch_theory |
| gptkbp:bfsLayer |
7
|