specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves M g ,...

There are inclusions: schemes ⊆ algebraic spaces ⊆ Deligne–Mumford stacks ⊆ algebraic stacks (Artin stacks) ⊆ stacks. Edidin (2003) and Fantechi (2001)...

mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric...

In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety...

In algebraic geometry, a quasi-coherent sheaf on an algebraic stack X {\displaystyle {\mathfrak {X}}} is a generalization of a quasi-coherent sheaf on...

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism...

In algebraic geometry, given algebraic stacks p : X → C , q : Y → C {\displaystyle p:X\to C,\,q:Y\to C} over a base category C, a morphism f : X → Y {\displaystyle...

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

In algebraic geometry, the quotient space of an algebraic stack F, denoted by |F|, is a topological space which as a set is the set of all integral substacks...

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,...

Jacobian Moduli of algebraic curves Hurwitz's theorem on automorphisms of a curve Clifford's theorem on special divisors Gonality of an algebraic curve Weil reciprocity...

GTK 3 algebraic and RPN calculator". galculator.mnim.org. Retrieved 2024-01-05. Schrijver, Frans. "Home - mouseless Stack-Calculator". www.stack-calculator...

or M e l l {\displaystyle {\mathcal {M}}_{\mathrm {ell} }} , is an algebraic stack over Spec ( Z ) {\displaystyle {\text{Spec}}(\mathbb {Z} )} classifying...

that X is quasi-separated as part of the definition of an algebraic space or algebraic stack X. Quasi-separated morphisms were introduced by Grothendieck...

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

In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking...

values in categories rather than sets Algebraic stack, a special kind of stack commonly used in algebraic geometry Stacks Project, an open source collaborative...

a separated algebraic stack, which is roughly a "best possible" approximation to the stack by a separated algebraic space. All algebraic spaces are assumed...

mathematics, especially algebraic geometry and algebraic topology, a higher stack is a higher category generalization of a stack (a category-valued sheaf)...

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

group-stack. More generally, a group algebraic-space, an algebraic-space analog of a group scheme, is a group-stack. Over a field k, a vector bundle stack V...

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

In algebraic geometry, the moduli stack of rank-n vector bundles Vectn is the stack parametrizing vector bundles (or locally free sheaves) of rank n over...

topological spaces Quotient space (linear algebra), in case of vector spaces Quotient space of an algebraic stack Quotient metric space Quotient object This...

The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry...

theory of non-abelian bundle gerbes. Twisted sheaf Azumaya algebra Twisted K-theory Algebraic stack Bundle gerbe String group Basic bundle theory and K-cohomology...

algebraic set (the length of such a chain is the number of " ⊊ {\displaystyle \subsetneq } "). Each variety can be considered as an algebraic stack,...

the moduli stack of principal bundles over X, denoted by Bun G ⁡ ( X ) {\displaystyle \operatorname {Bun} _{G}(X)} , is an algebraic stack given by: for...

ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings...

λ-ring AB5 category Abelian category Accessible category Algebraic geometry Algebraic stack Approximation property – Mathematical concept Barsotti–Tate...