Timeline for Arc space & formal loops in motivic integration
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2020 at 19:21 | vote | accept | user267839 | ||
| Mar 19, 2020 at 16:42 | answer | added | S. Carnahan♦ | timeline score: 4 | |
| Mar 19, 2020 at 1:19 | comment | added | Asvin | Spec C[[t]] is like a formal neighborhood of the origin in the complex plane and inverting t corresponds to puncturing at the origin. | |
| Mar 18, 2020 at 21:33 | comment | added | user267839 | @xir: a further point is that you claim that "$k((t))$ seems to have a spectrum like a punctured disk." I'm not sure what you mean at this point. It's a spectrum of a field, thus a single point, or not? In which way you interpret the spectrum of $k((t))$ to be like a punctured disc? | |
| Mar 18, 2020 at 21:22 | comment | added | xir | i've only encountered spaces of loops, and they've been $k((t))$ points in every case for me. arcs could be different from the sound of it. | |
| Mar 18, 2020 at 21:11 | comment | added | user267839 | by the way is for you in this context "space of loops" the same as "space of arcs"? | |
| Mar 18, 2020 at 21:05 | comment | added | user267839 | @xir: I'm quite sure that what I'm wrote should be correct. This is my source: arxiv.org/abs/1604.02728 (see page 2). De Fernex write: "The space of arcs of $X$ is a scheme whose $K$-valued points, for any field extension $K/k$, are formal arcs $\alpha: Spec \ K[[t]] \to X$." | |
| Mar 18, 2020 at 20:00 | comment | added | xir | are you sure that the "space of loops" isn't given by taking $k((t))$-points instead? $k((t))$ seems to have a spectrum like a punctured disk (so a loop) topologically, but $k[[t]]$ seems more like just a disk. | |
| Mar 18, 2020 at 18:55 | history | edited | user267839 | CC BY-SA 4.0 |
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| Mar 18, 2020 at 17:19 | history | edited | user267839 | CC BY-SA 4.0 |
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| Mar 18, 2020 at 16:58 | history | asked | user267839 | CC BY-SA 4.0 |