Timeline for Sheaf whose singular support is not Lagrangian
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 18, 2017 at 19:20 | comment | added | Piotr Achinger | Also no I don't think there is a simpler example than an Artin-Schreier sheaf on $\mathbb{A}^2$ ;) Of course your sheaf has generically rank $p$, but it splits into rank one sheaves (Artin-Schreier sheaves for characters $\mathbb{F}_p\to \mathbb{F}_\ell^\times$) and you can take each of those except for the constant one. | |
| Sep 18, 2017 at 19:19 | comment | added | Piotr Achinger | I think the point is that in characteristic $p$, $t^p - t = xy^{p-1}$ is fiercely ramified at infinity (purely inseparable extension of the residue field). For $p=2$ this is your example. It's probably correct but I don't remember the computation. It also appears in my paper "Wild ramification and K(pi, 1) spaces" section 7.1 as an example for something closely related, and you should be able to deduce what you want combining it with Remark 3.3 in the same paper. By the way, I think Deligne showed that for surfaces you can get any closed two-dim conical subset you want as the singular support. | |
| Sep 18, 2017 at 14:58 | history | asked | John Pardon | CC BY-SA 3.0 |