scheme theory

Noun

scheme theory (uncountable)

1. Used other than figuratively or idiomatically: see scheme, theory.
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).
   • 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.1997, Kenji Ueno, translated by Goro Kato, Algebraic Geometry 1: From Algebraic Varieties to Schemes, American Mathematical Society, page x
   • 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...1999, Freddy Van Oystaeyen, “A Deformation of Projective Schemes”, in Freddy Van Oystaeyen, editor, Commutative Algebra and Algebraic Geometry, Marcel Dekker, page 295
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.
   • With these ideas of scheme theory, perturbation, and abstraction, it becomes possible to see how metacognition might be interpreted in constructivist terms.1998, Douglas J. Hacker, Metacognition in Educational Theory and Practice, page 78