Grothendieck duality

E254134
duality theory theory in algebraic geometry

Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (3)

Label Occurrences
Grothendieck duality canonical 1
Grothendieck duality theory 1
Grothendieck–Verdier duality 1

Statements (50)

Predicate Object
instanceOf duality theory ⓘ
theory in algebraic geometry ⓘ
appliesTo finite morphisms of schemes ⓘ
morphisms of schemes ⓘ
proper morphisms of schemes ⓘ
schemes ⓘ
smooth morphisms of schemes ⓘ
centralConcept adjoint functors ⓘ
derived categories ⓘ
dualizing complex ⓘ
extraordinary inverse image functor ⓘ
context coherent sheaves ⓘ
finite type morphisms ⓘ
proper morphisms of schemes ⓘ
quasi-coherent sheaves ⓘ
developedBy Alexander Grothendieck ⓘ
developedIn EGA ⓘ
SGA ⓘ
field algebraic geometry ⓘ
formalism six functors formalism ⓘ
frameworkType categorical ⓘ
sheaf-theoretic ⓘ
furtherDevelopedBy Amnon Neeman ⓘ
Brian Conrad ⓘ
Joseph Lipman ⓘ
Robin Hartshorne ⓘ
generalizes Serre duality ⓘ
goal to express cohomology in terms of dual objects ⓘ
to generalize classical duality on varieties ⓘ
hasAspect absolute duality ⓘ
relative duality ⓘ
hasGeneralization non-noetherian duality theories ⓘ
involves base change theorems ⓘ
bounded derived category of coherent sheaves ⓘ
perfect complexes ⓘ
trace morphisms ⓘ
namedAfter Alexander Grothendieck ⓘ
provides global duality statements ⓘ
local duality statements ⓘ
relative duality for morphisms ⓘ
relatedConcept Serre duality ⓘ
Verdier duality ⓘ
canonical sheaf ⓘ
dualizing sheaf ⓘ
requires noetherian hypotheses in classical form ⓘ
usedIn birational geometry ⓘ
intersection theory ⓘ
moduli theory ⓘ
usesFunctor derived direct image functor Rf_* ⓘ
extraordinary inverse image functor f^! ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Alexander Grothendieck → notableConcept → Grothendieck duality ⓘ
Serre duality → involves → Grothendieck duality ⓘ
this entity surface form: Grothendieck duality theory
Serre duality → isSpecialCaseOf → Grothendieck duality ⓘ
this entity surface form: Grothendieck–Verdier duality