mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated...
43 KB (6,691 words) - 21:02, 23 March 2024
In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of...
19 KB (2,923 words) - 15:42, 22 August 2024
specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic...
51 KB (9,805 words) - 12:43, 5 June 2024
Hodge theory (redirect from Hodge cohomology)
Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations. The...
28 KB (4,309 words) - 16:21, 17 August 2024
Motive (algebraic geometry) (redirect from Universal Weil cohomology)
similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology. Philosophically,...
33 KB (4,920 words) - 14:54, 23 June 2024
coefficient theorems establish relationships between homology groups (or cohomology groups) with different coefficients. For instance, for every topological...
8 KB (1,181 words) - 13:40, 29 June 2023
In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients...
33 KB (5,016 words) - 17:10, 20 January 2024
In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking...
36 KB (5,832 words) - 15:01, 25 July 2024
Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the...
16 KB (2,285 words) - 19:58, 29 December 2023
Eichler–Shimura isomorphism (redirect from Eichler cohomology)
In mathematics, Eichler cohomology (also called parabolic cohomology or cuspidal cohomology) is a cohomology theory for Fuchsian groups, introduced by...
4 KB (418 words) - 14:22, 15 March 2024