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Results tagged with motives
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user 2481
for questions about motives in algebraic geometry, including constructions of categories of motives and motivic sheaves, and aspects of the standard conjectures.
1
vote
critical values of motives
In your example (with Hodge structure of weight 3 concentrated in bidegrees (2, 1) and (1, 2)) there is only one critical value, at s = 2. At all other integer values of $s$, either $L_\infty(M, s)$ o …
- 37k
8
votes
Accepted
Difference of Beilinson conjecture and equivariant Tamagawa number conjecture
(You could also formulate an "equivariant Beilinson conjecture" involving $\mathbf{Q}[G]$-modules, but it would be fairly trivally equivalent to the original Beilinson conjecture for each of the motives …
- 37k
4
votes
Motive of CM elliptic curve and modular forms
These motives really should be the same, because their $\ell$-adic Galois representations are the same for every $\ell$, but there is (as far as I know) no natural way of writing down a correspondence … that gives an isomorphism between them in the category of Chow motives. …
- 37k
3
votes
Accepted
Motive associated to a cuspidal representation of $GSp_{4}$
The first problem was solved by Wildeshaus using his theory of "interior motives". This gives a Grothendieck motive attached to pi, but sadly not a Chow motive, because of the second problem above. …
- 37k
11
votes
1
answer
916
views
Motivic cohomology and pushforward maps
For étale cohomology, the work of Ciskinski--Deglise "Etale motives" apparently gives a realisation functor (on some category of motivic complexes) that is "compatible with Grothendieck's six operations …
- 37k
9
votes
Accepted
"Weight-monodromy" for open varieties
Tony Scholl gave a talk at a conference in Warwick in 2013 on exactly this topic (his talk was called "Remarks on monodromy and weights"). He explained how to formulate a precise version of weight-mon …
- 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