Timeline for perfect fields in positive characteristic
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 14, 2021 at 2:20 | comment | added | SashaP | Galois theory of perfect fields is, in fact, as hard as the Galois theory of general fields: if $k$ is a file of characteristic $p$ then its finite separable extensions are in bijection with finite (necessarily separable) extensions of its perfection $k_{perf}=colim(k\xrightarrow{x\mapsto x^p} k\to \dots)$ | |
| Apr 13, 2021 at 20:24 | history | became hot network question | |||
| Apr 13, 2021 at 14:13 | history | edited | JNS | CC BY-SA 4.0 |
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| Apr 13, 2021 at 13:31 | comment | added | Emil Jeřábek | Your example field is in fact already a counterexample. For instance, where is the $l$-th root of $x$ for prime $l\ne p$? | |
| Apr 13, 2021 at 12:54 | vote | accept | JNS | ||
| Apr 13, 2021 at 12:46 | answer | added | YCor | timeline score: 11 | |
| Apr 13, 2021 at 12:40 | comment | added | JNS | Yes, I meant same degree, thanks. I edited it. | |
| Apr 13, 2021 at 12:39 | history | edited | JNS | CC BY-SA 4.0 |
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| Apr 13, 2021 at 12:37 | comment | added | LSpice | Presumably, in (2), you want $L$ and $L'$ to be of the same degree? The property you are asking for seems closely related to being quasi-finite. | |
| Apr 13, 2021 at 12:23 | history | asked | JNS | CC BY-SA 4.0 |