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Results tagged with algebraic-cycles
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user 2481
7
votes
Accepted
Comparison of cycle maps
Everything you could wish for is true :-). Passing to the inverse limit in Milne's theorem 21.1 one gets an isomorphism
$$ H^i_{et}(X, \mathbf{Z}_\ell) = H^i_{sing}(X(\mathbf{C}), \mathbf{Z}) \otimes …
- 37k
4
votes
Accepted
Higher Chow cycles
There is a rather concrete construction in Landsburg's 1991 paper "Relative Chow groups" which gives an explicit isomorphism from $CH^k(X, 1)$ to the degree 1 homology of the Gersten complex, which is …
- 37k
15
votes
Accepted
Why can Euler systems constructed from algebraic cycles only be anticyclotomic?
Let me explain a bit more what that footnote was supposed to mean.
As I'm sure you know, an Euler system for a Galois representation $V$ over a number field $K$ consists of a bunch of classes in $H^1 …
- 37k
12
votes
Chow Groups of varieties over number fields
The statement you want follows fairly straightforwardly from Bass' conjecture -- sufficiently straightforwardly that it may well not have a separate name of its own.
If $\Sigma$ is a sufficiently lar …
- 37k