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Results tagged with cohomology
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user 5015
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, ...
16
votes
Galois cohomologies of an elliptic curve
When thinking of cohomology as describing a defect to a functor being exact, it has to be expected that the first few $H^i$ appear more often. … But in fact most of the above is not specific to elliptic curves and a book like "Cohomology of number fields" will describe this in all details. …
- 8,945
3
votes
Accepted
Is $H^{1}_{Sel}\left(K,E_{p^{n}}\right)\rightarrow\prod_{q \nmid \infty} H^1\left(K_{q},E_{p...
The answer is "no" in general.
By the definition of the Selmer group, you can replace the target of the map by the product of $E(K_q)/p^n E(K_q)$. Now $E(K)/p^n E(K)$ is a subgroup of the Selmer gro …
- 8,945
3
votes
applications of Tate-Poitou duality
An Euler system produces a collection of "derived" global cohomology classes. … I would suspect there are more examples in "Cohomology of Number Fields". …