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Results tagged with cohomology
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user 2284
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, ...
15
votes
"Gross-Zagier" formulae outside of number theory
It is tempting to speculate that Kudla's program type result (and the Gross-Zagier formula) could likewise follow from a study of the $p$-adic variation under deformation of the determinant of étale cohomology … At present, this is certainly backwards, in the sense that we usually prove results about the determinant of the cohomology using intersection of cycles on Shimura varieties and not the other way around …
- 10.9k
9
votes
Accepted
Why does $\mathbb C_p$ not contain the periods?
Consider the Tate motive $\mathbb Q(1)$. Its de Rham realization is simply $\mathbb Q$ (with the filtration $F^{-1}\mathbb Q=\mathbb Q$ and $F^{0}=0$) and its Betti realization is $2\pi i\mathbb Q$. T …
- 10.9k