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K-theory involves the construction of families of K-functors that map from topological spaces or schemes, or to be even more general: any object of a homotopy category to associated rings; these rings reflect some aspects of the structure of the original spaces or schemes.
Algebraic K-theory is a subject area in mathematics with connections ... the group K 2 (F) is related to class field theory, ... (PDF), Handbook of K-theory, Berlin, ...
Tensor product of bundles gives K-theory a commutative ring structure. Without subscripts, () usually denotes complex K-theory whereas real K-theory is sometimes written as (). The remaining discussion is focused on complex K-theory. As a first example, note that the K-theory of a point is the integers. This is because vector bundles over a ...
Download as PDF; Printable version ... In mathematics, Milnor K-theory [1] is an algebraic invariant ... plays a fundamental role in higher class field theory, ...
Download as PDF; Printable version; In other projects ... K-theory classification refers to a conjectured ... where P is an unknown characteristic class that depends ...
In algebraic K-theory, the K-theory of a category C (usually equipped with some kind of additional data) is a sequence of abelian groups K i (C) associated to it.If C is an abelian category, there is no need for extra data, but in general it only makes sense to speak of K-theory after specifying on C a structure of an exact category, or of a Waldhausen category, or of a dg-category, or ...
The K-groups of finite fields are one of the few cases where the K-theory is known completely: [2] for , = (() +) {/ (), =,For n=2, this can be seen from Matsumoto's theorem, in higher degrees it was computed by Quillen in conjunction with his work on the Adams conjecture.
The Brauer group plays an important role in the modern formulation of class field theory. If K v is a non-Archimedean local field, local class field theory gives a canonical isomorphism inv v : Br K v → Q/Z, the Hasse invariant. [2] The case of a global field K (such as a number field) is addressed by global class field theory.