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 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...

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...

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...

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...

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

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...

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...

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,...

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

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...

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: ...

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

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...

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...

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

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...

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

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...

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...

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...

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...

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...

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...

vector bundles that he defined. The fundamental group scheme is also known as Nori fundamental group scheme, taking the name by his creator, and often also...