Timeline for Is $\mathbb{P}^1$ the only smooth projective curve with a locally split tangent lie algebroid?
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| Apr 23, 2017 at 13:54 | comment | added | nfdc23 | The Zariski-local structure of smooth morphisms as in Will Sawin's answer (i.e., etale onto an affine space) is absolutely crucial for developing the theory of smooth morphisms and the robustness of the etale topology (e.g., proving many theorems in etale cohomology), being one of several equivalent characterizations (the proof of equivalences among which is far from elementary). That semistable singularities don't generally admit a Zariski neighborhood etale onto the model situation (only an etale neighborhood, by Artin approximation) makes them more subtle to study rigorously. | |
| Apr 23, 2017 at 2:11 | vote | accept | Saal Hardali | ||
| Apr 23, 2017 at 1:08 | answer | added | Will Sawin | timeline score: 4 | |
| Apr 22, 2017 at 22:33 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Apr 22, 2017 at 22:28 | history | edited | Saal Hardali | CC BY-SA 3.0 |
added 8 characters in body
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| Apr 22, 2017 at 22:26 | history | asked | Saal Hardali | CC BY-SA 3.0 |