Timeline for Cotangent complex of perfect algebra over a perfect field
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2018 at 3:40 | answer | added | Jacob Lurie | timeline score: 7 | |
| Dec 30, 2017 at 19:05 | history | edited | A Rock and a Hard Place | CC BY-SA 3.0 |
Fixed typo in title.
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| Dec 30, 2017 at 19:04 | vote | accept | A Rock and a Hard Place | ||
| Dec 30, 2017 at 14:29 | answer | added | user117273 | timeline score: 7 | |
| Dec 30, 2017 at 11:23 | comment | added | A Rock and a Hard Place | There is certainly Theorem HA.7.4.3.18 (HA = Higher Algebra), saying that $L_{B/A}$ is (almost) perfect if $A\to B$ is quite generally an (almost) finitely presented map of connected $\mathbb E_\infty$-rings. However the converse is only stated under the assumption that $\pi_0A\to \pi_0B$ if finitely presented. Based on that, there might still be a chance for $L_{B/A}$ to be (almost) perfect even if $A\to B$ fails the finiteness condition, so long as the underlying map $\pi_0A\to \pi_0B$ also fails it. | |
| Dec 30, 2017 at 9:29 | comment | added | Denis Nardin | If I recall correctly finiteness results are true under the hypotheses that $A$ is a finitely presented $E_\infty$-algebra over $\kappa$. I don't think that's true very often unfortunately | |
| Dec 30, 2017 at 8:23 | history | asked | A Rock and a Hard Place | CC BY-SA 3.0 |