Timeline for Are there known cases of the Mumford–Tate conjecture that do not use Abelian varieties?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 26, 2014 at 9:54 | vote | accept | jmc | ||
| Nov 26, 2014 at 5:43 | answer | added | naf | timeline score: 11 | |
| Nov 25, 2014 at 12:08 | comment | added | jmc | @ulrich – Thanks for your comment! Would you mind posting it as an answer (together with references to Ribet and Blasius)? Then I can accept it, and therewith mark this question as “Solved”. | |
| Nov 25, 2014 at 3:58 | comment | added | naf | I think the work of Ribet on the image of the Galois representation associated to modular forms implies the Mumford-Tate conjecture for the corresponding motives. Blasius has shown that not all these motives are in LCM. | |
| Nov 24, 2014 at 17:19 | history | edited | jmc | CC BY-SA 3.0 |
Clarified a bit
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| Nov 24, 2014 at 16:54 | answer | added | Daniel Loughran | timeline score: 8 | |
| Nov 24, 2014 at 15:37 | comment | added | jmc | @SimonPepinLehalleur — Ben Moonen is indeed my advisor. I indeed know of this result, but since there is no reference yet I didn't mention it. And, like you say, it is still based on Kuga–Satake. I totally agree with you that it is a non-trivial variation. However, since I was able to overlook the results of Zhao on AV's of dimension 4 until last week, I wondered if there might be any results that do not go back to AV's. (Btw, the MT-conj is true for the generic variety; since the MT-grp and the Gal-grp are generically both the full symplectic (resp. orthogonal) grp for $i$ odd (resp. even). | |
| Nov 24, 2014 at 14:58 | comment | added | Simon Pepin Lehalleur | Ben Moonen (which if I understand correctly is your advisor; this is a comment for onlookers) gave a great talk recently on the Mumford-Tate conjecture for divisors which he can prove for many surfaces with h^{2,0}=1 beyond the K3 case. It is still based on Kuga-Satake, hence at the end of the day Hodge theory for abelian varieties (plus the machinery of Deligne and André on deformation of absolute Hodge/motivated classes). It is still a rather non-trivial variation on the K3 case. | |
| Nov 24, 2014 at 14:17 | history | asked | jmc | CC BY-SA 3.0 |