Timeline for The Shafarevich Conjecture and motivic Langlands stacks.
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2011 at 6:07 | comment | added | S. Carnahan♦ | One minor detail: $\mathcal{M}_{1,1}$ is not proper, and it is really easy to construct hyperbolic curves that aren't proper, even without using stacks. The Deligne-Mumford compactification has Picard group $\mathbb{Z} \times \mathbb{Z}/12\mathbb{Z}$. | |
| Nov 30, 2011 at 4:49 | comment | added | Spaghetti Inks | Naturally $X/k$ is the notation, I say to old Qfwfq, what else could it have been? | |
| Nov 30, 2011 at 4:48 | comment | added | Spaghetti Inks | Dear Professor Carnahan, I would love it if you could explain the construction ("it is not too difficult to make genus zero curves with .. good reudction everywhere"). | |
| Nov 30, 2011 at 2:28 | comment | added | S. Carnahan♦ | I don't see why you would expect the pullback of motives attached to a coarse moduli map to be an isomorphism. Integrality is inherent in basically all modern treatments (see Levine's book, Voevodsky's papers, etc.). Also, it is not too difficult to make twisted genus zero curves with negative Euler characteristic and "good reduction" everywhere. | |
| Nov 29, 2011 at 10:07 | comment | added | Qfwfq | (If the "Worst notation ever" question was still open, I would add the notation " $X/k$ " often used by algebraic geometers to mean "the scheme $X$ is defined over $k$"!) | |
| Nov 29, 2011 at 6:00 | comment | added | Chandan Singh Dalawat | I provided the links merely because they discuss the relationship of the Langlands' Programme with Fontaine-Abrashkin. | |
| Nov 29, 2011 at 4:10 | comment | added | Spaghetti Inks | Dear Professor Dalawat - thanks for the links! This is addressing the last question I presume? If I understand you, you are saying that the "1-motive" should be an abelian variety over $\mathbf{Z}$ which can't exist. But I was thinking along the following lines: is there some integral "Motivic like" object $[\mathcal{M}]$ for which "$H^1$" returned $\mathbf{Z}/\mathbf{Z}12$. I don't even know if Motives are supposed to form a category with "integral" properties... and maybe this is related to "torsion" automorphic forms... perhaps your remarks merely expose my ignorance, but I like to dream! | |
| Nov 29, 2011 at 2:42 | comment | added | Chandan Singh Dalawat | mathoverflow.net/questions/10860/… | |
| Nov 29, 2011 at 2:41 | comment | added | Chandan Singh Dalawat | mathoverflow.net/questions/31538/… | |
| Nov 29, 2011 at 1:40 | history | asked | Spaghetti Inks | CC BY-SA 3.0 |