Scheme (mathematics)

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Scheme (mathematics) แนวคิดใหม่
Grothendieck กำหนดใน 1960
จึงขอจาร ขานเขียน สักจิบจิบ
อย่ายากลิบ วิบหาย กับสายลม

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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 x^2 = 0 define the same algebraic variety and different schemes)
and allowing "varieties" defined over any commutative ring
(for example, Fermat curves are defined over the integers).

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Formally,
a scheme is a topological space together with commutative rings for all of its open sets,
which arises from gluing together spectra (spaces of prime ideals) of commutative rings along their open subsets.

In other words, it is a ringed space which is locally a spectrum of a commutative ring.