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

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

called Serre–Grothendieck–Verdier duality, and is a basic tool in algebraic geometry. A treatment of this theory, Residues and Duality (1966) by Robin...

connection Grothendieck construction Grothendieck duality Grothendieck existence theorem Grothendieck fibration Grothendieck's Galois theory Grothendieck group...

mathematics, local duality may refer to: Local Tate duality of modules over a Galois group of a local field Grothendieck local duality of modules over local rings...

Tannaka–Krein duality Verdier duality Grothendieck local duality Dualism (philosophy of mind) Epistemological dualism Dualistic cosmology Soul dualism Yin and...

Alexander Grothendieck (/ˈɡroʊtəndiːk/; German pronunciation: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ; French: [ɡʁɔtɛndik]; 28 March 1928 – 13 November 2014) was...

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

scheme is Gorenstein. Thus the statements of duality theorems such as Serre duality or Grothendieck local duality for Gorenstein or Cohen–Macaulay schemes...

R with some degree shift. For a Gorenstein local ring (R, m, k) of dimension n, Grothendieck local duality takes the following form. Let E(k) be the injective...

the canonical bundle of a smooth variety. It is used in Grothendieck local duality. A dualizing module for a Noetherian ring R is a finitely generated...

Matlis duality is a duality between Artinian and Noetherian modules over a complete Noetherian local ring. In the special case when the local ring has...

instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and...

characteristic zero. global dimension bar resolution Grothendieck group Grothendieck local duality Weibel (1999); Cartan & Eilenberg (1956), section VI...

D_{Y}(f_{*}M)\cong f_{!}(D_{X}(M)).} Coherent duality Grothendieck local duality Image functors for sheaves Verdier duality Change of rings Gallauer, Martin (2021)...

duality dualizing 1.  Grothendieck local duality is a duality for cohomology of modules over a local ring. 2.  Matlis duality is a duality between Artinian...

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

In algebraic geometry, local cohomology is an algebraic analogue of relative cohomology. Alexander Grothendieck introduced it in seminars in Harvard in...

replaced by discs of positive radius. Cartier duality is a scheme-theoretic analogue of Pontryagin duality taking finite commutative group schemes to finite...

many cases there is a duality theory for sheaves that generalizes Poincaré duality. See Grothendieck duality and Verdier duality. The derived category...

duality theorem; a result on topological groups. This (in rather special cases) provided an interpretation of Poincaré duality and Alexander duality in...

theorem Grothendieck–Riemann–Roch theorem Coherent duality Dévissage Affine scheme Scheme Éléments de géométrie algébrique Grothendieck's Séminaire...

algebraic varieties were subsumed into Alexander Grothendieck's concept of a scheme. Their local objects are affine schemes or prime spectra, which...

prove general results such as Poincaré duality and the Lefschetz fixed-point theorem in this context. Grothendieck originally developed étale cohomology...

space. The dream of noncommutative geometry is to generalize this duality to the duality between noncommutative algebras, or sheaves of noncommutative algebras...

smooth morphism. Then the virtual tangent bundle is an element of the Grothendieck group of vector bundles on X given as: T f = [ i ∗ T P / Y ] − [ N X...

In mathematics, the flat topology is a Grothendieck topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also plays...

proved by Bernard Dwork (1960), the functional equation by Alexander Grothendieck (1965), and the analogue of the Riemann hypothesis by Pierre Deligne (1974)...

géométrie algébrique ("Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné), or EGA for short, is a rigorous treatise...

with a single object. In his Tōhoku article, Grothendieck listed four additional axioms (and their duals) that an abelian category A might satisfy. These...