scheme theory

English

Noun

scheme theory (uncountable)

1. Used other than figuratively or idiomatically: see scheme,‎ theory.
2. (algebraic geometry) The branch of mathematics that concerns schemes (locally ringed spaces admitting coverings by open sets, each isomorphic to the spectrum of some commutative ring).
   • 1997, Kenji Ueno, translated by Goro Kato, Algebraic Geometry 1: From Algebraic Varieties to Schemes, American Mathematical Society, page x:

     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.

   • 1999, Freddy Van Oystaeyen, “A Deformation of Projective Schemes”, in Freddy Van Oystaeyen, editor, Commutative Algebra and Algebraic Geometry, Marcel Dekker, page 295:

     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.

   • 2004, Haruzo Hida, p-Adic Automorphic Forms on Shimura Varieties, Springer, page 68:

     The main point of scheme theory is to consider $C$ as a covariant functor $R\mapsto C(R)$ from the category ${\textit {B-ALG}}$ (also written as ${\textit {ALG}}_{/{\mathfrak {B}}}$) of ${\mathfrak {B}}$-algebras into the category ${\textit {SETS}}$ of sets.

3. (psychology) 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.
   • 1998, Douglas J. Hacker, Metacognition in Educational Theory and Practice, page 78:

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