What is scheme in math?
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety and different schemes) and allowing “varieties” defined over any commutative ring (for example.
Who founded mathematics scheme?
Alexander Grothendieck
The theory of schemes was pioneered by Alexander Grothendieck. The foundations of scheme theory were initially organized in Grothendieck’s multi-volume work Éléments de Géométrie Algébrique with the assistance of Jean Dieudonné.
What is a K scheme?
An algebraic k-scheme is a scheme X over k such that the structure morphism X \to \mathop{\mathrm{Spec}}(k) is of finite type. A locally algebraic k-scheme is a scheme X over k such that the structure morphism X \to \mathop{\mathrm{Spec}}(k) is locally of finite type.
What is a separated scheme?
A Separation Scheme tells you (or your lab partner) where your product and any by-products are at any point during the isolation of your final product from a chemical reaction.
Who developed schemes?
Scheme was created during the 1970s at the MIT AI Lab and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers.
Is a variety a scheme?
Definition 33.3. 1. Let k be a field. A variety is a scheme X over k such that X is integral and the structure morphism X \to \mathop{\mathrm{Spec}}(k) is separated and of finite type.
What is an integral scheme?
A scheme that is both reduced and irreducible is called integral. For locally Noetherian schemes, to be integral is equivalent to being a connected scheme that is covered by the spectra of integral domains.
What is the plural of scheme?
scheme. Plural. schemes. The plural form of scheme; more than one (kind of) scheme.
Are affine schemes separated?
Any morphism of affine schemes is separated. Recall that being separated means that the diagonal is a closed immersion. Since the latter is surjective, the corresponding map on schemes is a closed immersion.
What kind of mathematics is scheme based on?
Scheme (mathematics) Strongly based on commutative algebra, scheme theory allows a systematic use of methods of topology and homological algebra. Scheme theory also unifies algebraic geometry with much of number theory, which eventually led to Wiles’s proof of Fermat’s Last Theorem .
Which is the definition of a scheme over a field?
For a scheme Y, a scheme X over Y means a morphism X → Y of schemes. A scheme X over a commutative ring R means a morphism X → Spec ( R ). An algebraic variety over a field k can be defined as a scheme over k with certain properties.
Which is an example of a variety of a scheme?
For example, in studying algebraic surfaces, it can be useful to consider families of algebraic surfaces over any scheme Y. In many cases, the family of all varieties of a given type can itself be viewed as a variety or scheme, known as a moduli space .
Is there an open access Encyclopedia of mathematics?
The Encyclopedia of Mathematics wiki is an open access resource designed specifically for the mathematics community. The original articles are from the online Encyclopaedia of Mathematics, published by Kluwer Academic Publishers in 2002.