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  • Scheme (mathematics) - Wikipedia
    In mathematics, specifically algebraic geometry, a scheme is a 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 but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat
  • Why schemes? - MIT Mathematics
    1 Why schemes? Schemes were introduced by Grothendieck more than fty years ago into the world of algebraic geometry In much the same way as measure theory, nearly everyone in the eld almost immediately adopted the new de nitions But like measure theory for someone on the outside the whole theory seems remarkably abstract and hard to absorb For
  • Scheme - Encyclopedia of Mathematics
    A scheme is regular if all its local rings are regular (cf Regular ring (in commutative algebra)) Other schemes defined in the same way include normal and reduced schemes, as well as Cohen–Macaulay schemes A morphism of schemes is a morphism between them as locally ringed spaces
  • What is the use of scheme theory? - Mathematics Stack Exchange
    Grothendieck saw how to convert a ring into a space with a topology, a so-called affine scheme, and then defined schemes to be the things you can get by gluing together affine schemes
  • Introduction to Schemes - Purdue University
    The solution to all of these problems, due to Grothendieck, is to consider something more general called a scheme 1 The definition is pretty involved So let’s start by describing the basic building blocks called a ne schemes Recall that given an a ne variety X over algebraically closed field, we can associate the a ne domain R = O(X)
  • Section 26. 9 (01II): Schemes—The Stacks project - Columbia University
    26 9 Schemes historical remark Definition 26 9 1 A scheme is a locally ringed space with the property that every point has an open neighbourhood which is an affine scheme A morphism of schemes is a morphism of locally ringed spaces The category of schemes will be denoted $\mathit{Sch}$ Let $X$ be a scheme
  • What elementary problems can you solve with schemes?
    One key scheme theoretic player in E-V-W result is a certain type of scheme called Hurwitz scheme To read great stuff related to all this check: Ellenberg-Venkatesh, Statistics of Number Fields and Function Fields (Proceedings of ICM 2010)
  • scheme - PlanetMath. org
    A scheme is a locally ringed space (X, 𝒪 X) which has an open cover {U α} α ∈ I with the property that each open set U α, together with its restriction sheaf 𝒪 X | U α, is an affine scheme





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