Timeline for Chow group of a (particular) motive [+ reference request]
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2012 at 12:31 | vote | accept | jmc | ||
| Oct 19, 2012 at 11:06 | answer | added | Dan Petersen | timeline score: 3 | |
| Oct 19, 2012 at 6:21 | comment | added | jmc | @Dan I think you have answered my question pretty much. If you turn your comment into an answer, I can accept it. (Although Q1 still needs an answer, but I might be able to figure that out myself, now.) | |
| Oct 19, 2012 at 6:08 | comment | added | Dan Petersen | I haven't had time to read the actual question carefully, but here is an answer to Will's comment: if $X$ is a smooth projective variety and $h(X)$ its motive, then there are functorial isomorphisms $\mathrm{Hom}(h(X),\mathbb L^s) = \mathrm{CH}^s(X)$ and $\mathrm{Hom}(\mathbb L^s, h(X)) = \mathrm{CH}_s(X)$. Here $\mathbb L$ is the Tate motive $H^2(\mathbf P^1)$. | |
| Oct 19, 2012 at 2:55 | comment | added | jmc | Hmm, that seems to make sense. I am not yet very familiar with all this. So I will try to write it out for myself in a minute. Do you by chance have anything to say about Q1? Are you `surprised' by this definition, or are there other places in literature where I can read about this? | |
| Oct 19, 2012 at 1:48 | comment | added | Will Sawin | I mean, given a variety $X$ and an idempotent correspondence $e$ on it, $e$ acts by intersection on the Chow group as an idempotent, so the kernel of that correspondence should be the kernel of that action on the Chow group, and the cokernel should be the cokernel. I think that takes care of uniqueness. | |
| Oct 19, 2012 at 1:30 | comment | added | jmc | @Will I think that is what I am looking for. But I have no idea whether such a functor exists. Uniqueness would be a second issue. | |
| Oct 19, 2012 at 1:28 | history | edited | jmc | CC BY-SA 3.0 |
Made the reference request explicit.
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| Oct 19, 2012 at 1:05 | comment | added | Will Sawin | Is there a unique exact functor from the category of motives to abelian groups such that it takes a smooth projective variety to its Chow group and a morphism of smooth projective varieties to the pullback morphism on Chow groups? | |
| Oct 18, 2012 at 23:59 | history | asked | jmc | CC BY-SA 3.0 |