Statements (90)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:mathematics |
| gptkbp:appliesTo |
gptkb:moduli_problems
intersection theory deformation theory algebraic stacks |
| gptkbp:developedBy |
gptkb:Jacob_Lurie
gptkb:Vladimir_Drinfeld gptkb:Bertrand_Toën gptkb:Gabriele_Vezzosi |
| gptkbp:emergedIn |
early 2000s
|
| gptkbp:hasConcept |
gptkb:derived_Artin_stack
gptkb:derived_Deligne-Mumford_stack cotangent complex derived algebraic geometry over derived fiber product derived algebraic geometry over commutative ring spectra derived algebraic geometry over E-infinity rings derived algebraic geometry over cotangent complex derived algebraic geometry over derived categories derived algebraic geometry over derived pullback derived algebraic geometry over derived schemes derived algebraic geometry over derived stacks derived algebraic geometry over dg-rings derived algebraic geometry over higher categories derived algebraic geometry over higher stacks derived algebraic geometry over homotopy theory derived algebraic geometry over model categories derived algebraic geometry over spectra derived algebraic geometry over topological spaces derived algebraic geometry over ∞-categories derived algebraic group derived algebraic space derived algebraic stack derived algebraic variety derived base change derived critical locus derived deformation theory derived fiber product derived functors derived group scheme derived intersections derived loop space derived mapping stack derived moduli spaces derived moduli stack derived pullback derived pushforward derived ring derived scheme derived stack derived stack of perfect complexes derived symplectic structure derived tensor product higher stacks homotopy colimits homotopy limits quasi-coherent sheaves derived algebraic geometry over quasi-coherent sheaves shifted symplectic structure spectral algebra spectral algebraic geometry spectral moduli stack spectral scheme spectral sheaf spectral stack spectral topos derived algebraic geometry over derived pushforward derived algebraic geometry over derived deformation theory derived algebraic geometry over homological algebra derived algebraic geometry over derived intersections derived algebraic geometry over simplicial commutative rings derived algebraic geometry over derived moduli spaces derived algebraic geometry over derived tensor product ∞-topos derived algebraic geometry over derived base change |
| https://www.w3.org/2000/01/rdf-schema#label |
Derived Algebraic Geometry
|
| gptkbp:relatedTo |
gptkb:homotopical_algebraic_geometry
homological algebra classical algebraic geometry derived categories |
| gptkbp:studies |
higher category theory
derived schemes derived stacks |
| gptkbp:uses |
gptkb:∞-categories
gptkb:dg-algebras gptkb:simplicial_commutative_rings model categories homotopical methods |
| gptkbp:bfsParent |
gptkb:Jacob_Lurie
|
| gptkbp:bfsLayer |
6
|