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The equivariant algebraic K-theory is an algebraic K-theory associated to the category of equivariant coherent sheaves on an algebraic scheme with action of a linear algebraic group, via Quillen's Q-construction; thus, by definition,
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra.
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 ...
In mathematics, there are several theorems basic to algebraic K-theory. Throughout, for simplicity, we assume when an exact category is a subcategory of another exact category, we mean it is strictly full subcategory (i.e., isomorphism-closed.)
Operator K-theory is a generalization of topological K-theory, defined by means of vector bundles on locally compact Hausdorff spaces. Here, a vector bundle over a topological space X is associated to a projection in the C* algebra of matrix-valued—that is, ()-valued—continuous functions over X.
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "K-theory" The following 36 pages are in this category, out of 36 total.
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 theory K(0) agrees with singular homology with rational coefficients, whereas K(1) is a summand of mod-p complex K-theory. The theory K(n) has coefficient ring F p [v n,v n −1] where v n has degree 2(p n − 1). In particular, Morava K-theory is periodic with this period, in much the same way that complex K-theory has period 2.