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Download as PDF; Printable version; In other projects ... K-theory is, roughly speaking ... which is a free object in the category of coherent sheaves, ...
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.)
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 ...
The K-theory classification of D-branes has had numerous applications. For example, Hanany & Kol (2000) used it to argue that there are eight species of orientifold one-plane. Uranga (2001) applied the K-theory classification to derive new consistency conditions for flux compactifications.
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.
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 mathematics, Milnor K-theory [1] is an algebraic invariant (denoted () for a field) defined by John Milnor as an attempt to study higher algebraic K-theory in the special case of fields. It was hoped this would help illuminate the structure for algebraic K-theory and give some insight about its relationships with other parts of mathematics ...
Kurihara (1992) showed that the conjecture is equivalent to a statement in the algebraic K-theory of the integers, namely that K n (Z) = 0 whenever n is a multiple of 4. In fact from the Kummer–Vandiver conjecture and the norm residue isomorphism theorem follow a full conjectural calculation of the K -groups for all values of n ; see Quillen ...