WebAt Purposeful Maths we have worked to put together a 5-Year Scheme of Learning that is mapped to both the Key Stage 3 National Curriculum for England and the Pearson Edexcel GCSE Scheme of Learning. The aim of this Scheme of Learning is not be a definitive document that works for all schools; it is designed to be adapted for each school’s ... 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 x = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for … See more The origins of algebraic geometry mostly lie in the study of polynomial equations over the real numbers. By the 19th century, it became clear (notably in the work of Jean-Victor Poncelet and Bernhard Riemann) … See more Schemes form a category, with morphisms defined as morphisms of locally ringed spaces. (See also: morphism of schemes.) For a scheme Y, a … See more Here are some of the ways in which schemes go beyond older notions of algebraic varieties, and their significance. • Field … See more Grothendieck then gave the decisive definition of a scheme, bringing to a conclusion a generation of experimental suggestions and … See more An affine scheme is a locally ringed space isomorphic to the spectrum Spec(R) of a commutative ring R. A scheme is a locally ringed space X … See more Here and below, all the rings considered are commutative: • Every affine scheme Spec(R) is a scheme. • A … See more A central part of scheme theory is the notion of coherent sheaves, generalizing the notion of (algebraic) vector bundles. For a scheme X, one … See more

What is the use of scheme theory? - Mathematics Stack Exchange

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Scheme - Encyclopedia of Mathematics

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