Meaning of scheme theory | Babel Free

Definitions

1. Used other than figuratively or idiomatically: see scheme, theory.
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2. The branch of mathematics that concerns schemes (locally ringed spaces admitting coverings by open sets, each isomorphic to the spectrum of some commutative ring).
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3. A theory of group decision-making which explains group decisions as the result of a decision scheme on the initial distribution of attitudes in the group.
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Examples

“This book develops Grothendieck's scheme theory as a method for studying algebraic geometry.[…]In the preface of EGA [ Éléments de géométrie algébrique ], Grothendieck even claimed that a knowledge of classical algebraic geometry may hinder the reader from studying scheme theory.”

“There is another approach⟳ dealing with more ring⟳ theoretical objects, i.e. starting from a nice class of algebras, called schematic algebras, it is possible to define⟳ a space, a Zariski topology, points, lines etc..., cf. [VOW1], [AZ], [ATV]. then it becomes possible to develop⟳ a scheme theory, completely extending the theory of schemes in classical algebraic geometry.”

“The main point⟳ of scheme theory is to consider⟳ C as a covariant functor R#92;mapstoC(R) from the category #92;textit#123;B-ALG#125; (also written as #92;textit#123;ALG#125;#95;#123;#47;#92;mathfrak#123;B”

“With these ideas of scheme theory, perturbation, and abstraction, it becomes possible to see⟳ how metacognition might be interpreted in constructivist terms.”

CEFR level