English Dictionary

K-theory

名詞

不可算名詞 古風 廃用 可算名詞

(uncountable, algebra, algebraic geometry, algebraic topology) The study of rings R generated by the set of vector bundles over some topological space or scheme;

日本語の意味

K理論は、位相空間やスキーム上のベクトル束の集合から生成される環Rを対象に、その性質や構造を研究する分野であり、代数、代数幾何学、代数的位相幾何学などの分野と関連している。

K-theory provides a powerful framework for classifying vector bundles over complex projective varieties by using the Grothendieck ring of their isomorphism classes.

ベクトル束によって生成される環の理論は、同型類のグロタンディーク環を介して複素射影多様体上のベクトル束を分類するための強力な枠組みを提供する。

意味（1）

(uncountable, algebra, algebraic geometry, algebraic topology) The study of rings R generated by the set of vector bundles over some topological space or scheme;

K-theory as an independent discipline is a fairly new subject, only about 35 years old.

意味（2）

(dated, obsolete) that part of algebraic topology comprising what is now called topological K-theory.

意味（3）

(countable) The cohomology generated by the set of vector bundles over some topological space or scheme.

The theory of formal groups has found a number of rather spectacular applications in recent years in number theory, arithmetical algebraic geometry, algebraic geometry, and algebraic topology, ranging from congruences for the coefficients of modular forms and local class field theory to extraordinary K-theories and (indirectly) results on the homotopy groups of spheres.