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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.
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 …
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 …
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 …
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 …
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. …
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. …
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 …