Timeline for Is there a geometric realization of $\mathbf{C}((t))$-varieties?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2016 at 8:36 | history | edited | Mikhail Bondarko |
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| Dec 26, 2016 at 4:32 | comment | added | David Treumann | Hi David, I want (b) or something even stronger, but getting to (a) is already hard for me. | |
| Dec 25, 2016 at 23:57 | comment | added | David Roberts♦ | A minor point, but do you mean a) the (homotopy category of spaces) over the circle, or b) the homotopy category of (spaces over the circle)? They are potentially a little different. | |
| Dec 25, 2016 at 23:47 | answer | added | Will Sawin | timeline score: 8 | |
| Dec 25, 2016 at 10:13 | answer | added | Piotr Achinger | timeline score: 16 | |
| Dec 25, 2016 at 10:01 | comment | added | Piotr Achinger | Did you consider (1) finding a model over $\mathbb{C}[[t]]$, (2) applying Artin approximation? At least if your variety is smooth and proper, the topology of the general fiber should depend only on the model mod $t^N$ for some big $N$ (e.g. s.t. $t^N$ kills the torsion in $\Omega_{X/\mathbb{C}[[t]]}$). Apply Artin approximation to get a variety over $\mathbb{C}\{t\}$ (henselization), and hence over convergent power series. | |
| Dec 25, 2016 at 2:01 | history | asked | David Treumann | CC BY-SA 3.0 |