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...

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

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

Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic...

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...

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

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

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

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...

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

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

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...

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...

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...

standard in commutative algebra and algebraic geometry somewhat later, once the need was felt to adapt methods from calculus and geometry over the complex numbers...

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 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...

a {\displaystyle a} and every morphism in J {\displaystyle {\mathcal {J}}} to 1 a {\displaystyle 1_{a}} . The diagonal functor Δ : C → C J {\displaystyle...

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...

conditions are equivalent. There exists a morphism t : B → A such that t ∘ f is the identity on A. There exists a morphism u: C → B such that g ∘ u is the identity...

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

In algebraic geometry, a Deligne–Mumford stack is a stack F such that the diagonal morphism F → F × F {\displaystyle F\to F\times F} is representable,...

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

the set-theoretic sense: it is a closed immersion in the sense of algebraic geometry. That is, one can give a set of equations for the image. Except for...

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 →...

The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David...

functor which sends a set S to P(S) and a morphism f: S → T (here, a function between sets) to the image morphism. That is, for A = { x 1 , x 2 , . . . }...

category of supermanifolds. An algebraic group is a group object in the category of algebraic varieties. In modern algebraic geometry, one considers the more...

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...