In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex...

In mathematics, Grothendieck duality may refer to: Coherent duality of coherent sheaves Grothendieck local duality of modules over a local ring This disambiguation...

In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre...

instead, a duality called Verdier duality. Serre duality or coherent duality are similar to the statements above, but applies to cohomology of coherent sheaves...

duality and explains a very general instance thereof in detail. Probably the most general duality that is classically referred to as "Stone duality"...

came from the need to find a suitable formulation of Grothendieck's coherent duality theory. Derived categories have since become indispensable also outside...

uses the dualizing sheaf on the ambient Pn to construct the dualizing sheaf on X. coherent duality reflexive sheaf Gorenstein ring Dualizing module Hartshorne...

Grothendieck's coherent duality) one instance of Grothendieck's six operations formalism. Verdier duality generalises the classical Poincaré duality of manifolds...

functors with duality (see Verdier duality) can be used to obtain a high-brow explanation of Poincaré duality. In the context of quasi-coherent sheaves on...

if the dual of A is B, then the dual of B is A. Alexander duality Alvis–Curtis duality Artin–Verdier duality Beta-dual space Coherent duality Conjugate...

results on the vanishing of cohomology in various cases, duality theorems such as Serre duality, relations between topology and algebraic geometry such...

frame Projective transformation Fundamental theorem of projective geometry Duality (projective geometry) Real projective plane Real projective space Segre...

Mathematicians, was to formulate results on coherent duality, now going under the name "Grothendieck duality". Grothendieck, A. (1957), "Sur quelques points...

applications of derived categories included coherent duality and Verdier duality, which extends Poincaré duality to singular spaces. A shift or translation...

The dual of a family F ⊆ ℘(C) is the family F ⊥ of all subsets S ⊆ C orthogonal to every member of F, i.e., such that S ⊥ T for all T ∈ F. A coherent space...

types of coherentism: the coherence theory of truth, and the coherence theory of justification (also known as epistemic coherentism). Coherent truth is...

in terms of an inequality, known as Englert-Greenberger duality or simply wave-particle duality relation". See also ref 24 in this work. Hillmer, R.; Kwiat...

Cohen–Macaulay condition can be seen in coherent duality theory. A variety or scheme X is Cohen–Macaulay if the "dualizing complex", which a priori lies in the...

_{j}(-1)^{j}\dim _{k}(H^{j}(X,{\mathcal {O}}_{X})).} Serre duality is an analog of Poincaré duality for coherent sheaf cohomology. In this analogy, the canonical...

Grothendieck local duality is a duality theorem for cohomology of modules over local rings, analogous to Serre duality of coherent sheaves. Suppose that...

commutative ring. It is sometimes also called a coherent space because of the connection to coherent topoi. Let X be a topological space and let K ∘ {\displaystyle...

Two theories related by a duality need not be string theories. For example, Montonen–Olive duality is an example of an S-duality relationship between quantum...

cache coherency protocols such as the MESIF protocol attempt to reduce the communication required to maintain cache coherency. Scalable Coherent Interface...

a number of properties that a risk measure might or might not have. A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity...

(2009). "Notes on derived categories and Grothendieck duality" (PDF). Foundations of Grothendieck Duality for Diagrams of Schemes. Lecture Notes in Mathematics...

prototypical example of Koszul duality was introduced by Joseph Bernstein, Israel Gelfand, and Sergei Gelfand,. It establishes a duality between the derived category...

God or from the Demon. Duality with pluralism is considered a logical fallacy. Moral dualism began as a theological belief. Dualism was first seen implicitly...

and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules...

pair (Av, P). This association is a duality in the sense that there is a natural isomorphism between the double dual Avv and A (defined via the Poincaré...

dualizing complex See Coherent duality. dualizing sheaf On a projective Cohen–Macaulay scheme of pure dimension n, the dualizing sheaf is a coherent sheaf...