In the area of mathematics known as

K-theory In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, ...

, the Quillen spectral sequence, also called the Brown–Gersten–Quillen or BGQ spectral sequence (named after Kenneth Brown,

Stephen Gersten Stephen M. Gersten (born 2 December 1940) was an American mathematician, specializing in finitely presented groups and their geometric properties. Gersten graduated in 1961 with an AB from Princeton University and in 1965 with a PhD from Trinity C ...

, and

Daniel Quillen Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic ''K''-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 197 ...

), is a

spectral sequence In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by , they hav ...

converging to the

sheaf cohomology In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology describes the obstructions to solving a geometric problem globally when i ...

of a type of topological space that occurs in algebraic geometry. It is used in calculating the

homotopy In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a deforma ...

properties of a

simplicial group In mathematics, more precisely, in the theory of simplicial sets, a simplicial group is a simplicial object in the category of groups. Similarly, a simplicial abelian group is a simplicial object in the category of abelian groups. A simplicial group ...

References

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External links

A spectral sequence of Quillen
at the

Stacks Project The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them". , the book consists of 115 chapters (excluding the license and index ...

{{algebra-stub Algebraic K-theory