In algebraic geometry, given a morphism of schemes p : X → S {\displaystyle p:X\to S} , the diagonal morphism δ : X → X × S X {\displaystyle \delta :X\to...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast...

In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

Galois cohomology of algebraic groups, the spinor norm is a connecting homomorphism on cohomology. Writing μ2 for the algebraic group of square roots...

this notation, a Lie algebra can be defined as an object A {\displaystyle A} in the category of vector spaces together with a morphism [ ⋅ , ⋅ ] : A ⊗ A...

In algebraic geometry, a morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by...

enormous role in algebraic topology. Its influence has gradually expanded and presently includes commutative algebra, algebraic geometry, algebraic number theory...

Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local...

a projective variety under a morphism of algebraic varieties is closed for Zariski topology (that is, it is an algebraic set). This is a generalization...

abelian; the kernel of a morphism of vector bundles is in general not a vector bundle in any natural way.) A vector bundle morphism between vector bundles...

In algebraic geometry, a morphism of schemes f from X to Y is called quasi-separated if the diagonal map from X to X × YX is quasi-compact (meaning that...

deformed version of this Hopf algebra as describing a certain "non-standard" or "quantized" algebraic group (which is not an algebraic group at all). While there...

{\displaystyle F(X)} in D, associates each morphism f : X → Y {\displaystyle f\colon X\to Y} in C to a morphism F ( f ) : F ( X ) → F ( Y ) {\displaystyle...

In algebraic geometry, an unramified morphism is a morphism f : X → Y {\displaystyle f:X\to Y} of schemes such that (a) it is locally of finite presentation...

In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory...

operation is composition of permutations Regular map (algebraic geometry) – Morphism of algebraic varieties The words map, mapping, correspondence, and...

In algebraic geometry, the normal cone of a subscheme of a scheme is a scheme analogous to the normal bundle or tubular neighborhood in differential geometry...

topology on algebraic spaces. The Lis-Et topology has a subtle technical problem: a morphism between stacks does not in general give a morphism between the...

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric...

G-maps. The composition of two morphisms is again a morphism. If a morphism f is bijective, then its inverse is also a morphism. In this case f is called an...

In algebraic geometry and other areas of mathematics, an ideal sheaf (or sheaf of ideals) is the global analogue of an ideal in a ring. The ideal sheaves...

the mediating morphism u : Q → P above is not required to be unique. Pullbacks in differential geometry Equijoin in relational algebra Fiber product of...

In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves...

In algebraic geometry, given a morphism f: X → S of schemes, the cotangent sheaf on X is the sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules Ω...

every C-morphism f : FY → X, there is a unique D-morphism ΦY, X(f) = g : Y → GX such that the diagrams below commute, and for every D-morphism g : Y →...

algebraic invariants of topological spaces, the range of applications of homology and cohomology theories has spread throughout geometry and algebra....

In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point...

In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space...