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Results tagged with cohomology
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user 5952
A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...
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Singular homology of a graph.
We can define singular cohomology accordingly, and get then a natural pairing between homology and cohomology. … (c) Is there a Künneth morphism in singular cohomology? --is there a natural ring strucure on cohomology?
(d) What is a homotopy between morphisms of graphs? …
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Integral decomposition of the diagonal (Chow motives)
\ldots, e_n$ in the Chow group $\mathrm{CH}^d(X\times X)\otimes \mathbb Q$ which sum up to the diagonal $\Delta \subseteq X\times X$, and induce the projections $H^\ast(X,F) \to H^i(X,F)$ in any Weil cohomology … , say singular cohomology with $F=\mathbb Z$ and $\ell$-adic cohomology with $F = \mathbb Z_\ell$? …
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Lifting varieties to characteristic zero.
If that succeeds, compute de Rham cohomology of the lift over $W_k$ instead, which in general will be much easier to do. … Neglecting torsion, this de Rham cohomology is the same as the crystalline cohomology of $X$. …
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