a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and...

multiplicative group GL(1), considered as a group scheme. That is, for any integer n > 1 we can consider the morphism on the multiplicative group that takes...

of a group scheme is a generalization of a group action to a group scheme. Precisely, given a group S-scheme G, a left action of G on an S-scheme X is...

of abelian varieties. An abelian scheme over a base scheme S of relative dimension g is a proper, smooth group scheme over S whose geometric fibers are...

The Phoenician Scheme is a 2025 espionage black comedy film produced, written and directed by Wes Anderson from a story he conceived with Roman Coppola...

In mathematics, the fundamental group scheme is a group scheme canonically attached to a scheme over a Dedekind scheme (e.g. the spectrum of a field or...

group scheme is a certain kind of group scheme. A finite group scheme G {\displaystyle G} over a field K {\displaystyle K} is called an étale group scheme...

Equivalently, a linear algebraic group over k is a smooth affine group scheme over k. A connected linear algebraic group G {\displaystyle G} over an algebraically...

of the identity of the Weil group, which is quite complicated. The Weil–Deligne group scheme (or simply Weil–Deligne group) W′K of a non-archimedean local...

The Protection of Vulnerable Groups Scheme (PVGS) is a service offered by Disclosure Scotland to enable organisations in the public, private and Voluntary...

as a special case of schemes over k. In that language, a linear algebraic group G over a field k is a smooth closed subgroup scheme of GL(n) over k for...

generalizes a group scheme, which is a scheme whose sets of points have group structures in a compatible way. A group scheme is a group-stack. More generally...

X {\displaystyle X} a scheme. Moreover let G {\displaystyle G} be a group scheme over X {\displaystyle X} , a G {\displaystyle G} -torsor (or principal...

group functor is a group-valued functor on the category of commutative rings. Although it is typically viewed as a generalization of a group scheme,...

formal schemes that are larger than points. A smooth formal group scheme is a special case of a formal group scheme. Given a smooth formal group, one can...

The Group Settlement Scheme was an assisted migration scheme which operated in Western Australia from the early 1920s. It was engineered by Premier James...

simplicity, a reference to the base scheme is often omitted; i.e., a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism. Contents: ...

definition of an algebraic group over a field k {\displaystyle k} is that it is a group scheme over k {\displaystyle k} (group schemes can more generally be...

scheme (since the automorphism groups are defined by polynomials): this scheme is called the automorphism group scheme and is denoted by Aut ⁡ ( M ) {\displaystyle...

étale or algebraic fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces. In algebraic...

topological space. The identity component of a group scheme G over a base scheme S is, roughly speaking, the group scheme G0 whose fiber over the point s of S is...

x_{i>j}=0)}}\right)} and an affine group scheme is unipotent if it is a closed group scheme of this scheme. An element x of an affine algebraic group is unipotent when...

A Ponzi scheme (/ˈpɒnzi/, Italian: [ˈpontsi]) is a form of fraud that lures investors and pays profits to earlier investors with funds from more recent...

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

They are used for studying finite flat commutative group schemes. Finite flat commutative group schemes over a perfect field k {\displaystyle k} of positive...

arithmetic geometry, the Tate–Shafarevich group Ш(A/K) of an abelian variety A (or more generally a group scheme) defined over a number field K consists...

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

x)} for schemes defined over Dedekind schemes and they also defined, and proved the existence of, the quasi-finite fundamental group scheme π qf ( X...

ring construction. The group scheme GL 1 {\displaystyle \operatorname {GL} _{1}} is isomorphic to the multiplicative group scheme G m {\displaystyle \mathbb...

A pyramid scheme is a business model which, rather than earning money (or providing returns on investments) by sale of legitimate products to an end consumer...