étale Group Scheme
   HOME

TheInfoList



Click Here for Items Related To - étale Group Scheme
OR:
étale Group Scheme on:   [Wikipedia]   [Google]   [Amazon]

In
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, more precisely in
algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
, an étale group scheme is a certain kind of
group scheme In mathematics, 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 they generalize algebraic groups, in the sense that all algebraic groups hav ...
.


Definition

A finite
group scheme In mathematics, 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 they generalize algebraic groups, in the sense that all algebraic groups hav ...
G over a field K is called an ''étale group scheme'' if it is represented by an étale K-algebra \mathfrak, i.e. if \mathfrak\otimes _\bar is
isomorphic In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between the ...
to \bar\times ...\times\bar.


References

* {{DEFAULTSORT:Etale Group Scheme Algebraic groups Scheme theory