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Results tagged with motives
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user 43054
for questions about motives in algebraic geometry, including constructions of categories of motives and motivic sheaves, and aspects of the standard conjectures.
21
votes
Why presheaves with transfer?
I hope someone can provide a better answer with more of an eye towards the motivic world, but for now let me outline that the exact same phenomenon exists in classical stable homotopy theory. Here the …
- 16.5k
3
votes
Dualizability and motivic cohomology
For the equation you are asking about, you don't want $MA$ to be dualizable (which is lucky, because it's not), you want $MA\wedge X_+$ to be dualizable as an $MA$-module. This is true in the situatio …
- 16.5k
11
votes
Accepted
How to think about $\mathbf{Z}(n)_{\mathcal{M}}$
[All cohomology will be reduced cohomology for ease of notation].
There is no analog for classical homotopy theory. This is related to the fact that the Picard group of the category of spectra is $\m …
- 16.5k
15
votes
Accepted
How to think about infinite generatedness of motivic cohomology
While waiting for someone more competent than me to answer, let me turn the question right back to you. Why should motivic cohomology be finitely generated?
The answer is, of course, that there's no …
- 16.5k