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Results tagged with motives
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user 2284
for questions about motives in algebraic geometry, including constructions of categories of motives and motivic sheaves, and aspects of the standard conjectures.
6
votes
Status of conjectures in Serre's 1969 expose on Galois representations on l-adic cohomology
Because I recently had to think about this, let me sum up the results I know about conjecture C5.
This conjecture is known to hold for any $m\in\mathbb N$ if the dimension of $Y$ is less than 2 by Ta …
- 10.9k
7
votes
Accepted
Is Scholl construction of modular motives related to Deligne's construction of $\ell$-adic r...
More explicitly, I would like to know if from these motives $M_{f}$ I can create an $\ell$-adic representation with values in some object of cohomological nature arising from $M_{f}$ (like motivic cohomology …
- 10.9k
3
votes
Accepted
Do $Q_l$-etale Euler characteristics of Chow motives coincide for all $l$?
I might be missing something (seeing that I don't know what a Chow motive is), but I think the answer is yes. It is a result of G.Laumon proved in Comparaison de caractéristiques d’Euler-Poincaré en c …
- 10.9k
13
votes
Why would one "attempt" to define points of a motive as $\operatorname{Ext}^1(\mathbb{Q}(0),...
The works of P.Deligne, A.Beilinson, S.Bloch and K.Kato on special values of $L$-function of motives aimed at generalizing this lattice to general (putative) motives. … I am a bit puzzled by the "even" part of the remark as the category of mixed motives, if it exists and if all the conjectures about it are true (a rather bold requirement, admittedly), is of cohomological …
- 10.9k
5
votes
Langlands in dimension 2: the Yoshida conjecture
And so it turns out that I was in the audience of a seminar talk just today on this very subject. The opinion I expressed in comments is apparently not too far from the truth: V.Pilloni and B.Stroh no …
- 10.9k
2
votes
The historical development of automorphic geometry
A common answer to question 1 is to mention the entries of Gauss's diary from 1814, including famously (but not restricted to) the last one, in which he studies some properties of biquadratic reciproc …
- 10.9k