Timeline for Henselian valued fields for characteristic $0$: a characterization
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2020 at 13:38 | vote | accept | user267839 | ||
| Mar 11, 2020 at 5:23 | answer | added | nombre | timeline score: 4 | |
| Mar 10, 2020 at 20:54 | history | edited | Jérôme Poineau | CC BY-SA 4.0 |
corrected spelling in the title
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| Mar 10, 2020 at 17:47 | history | edited | user267839 | CC BY-SA 4.0 |
added 37 characters in body
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| Mar 10, 2020 at 17:37 | comment | added | user267839 | Yes the criterion I'm looking for is $K$ Henselian iff $K=K_v\cap \overline{K}$. Thanks! | |
| Mar 10, 2020 at 17:35 | history | edited | user267839 | CC BY-SA 4.0 |
added 2 characters in body; edited title
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| Mar 10, 2020 at 6:41 | comment | added | Arno Fehm | Probably you meant "K is henselian iff $K=K_v\cap\overline{K}$"? And by valuation you mean a map $v:K\rightarrow\mathbb{R}\cup\{\infty\}$ with the usual properties? Possibly the term you are looking for is "algebraically maximal". | |
| Mar 10, 2020 at 5:47 | comment | added | KConrad | Your second paragraph makes no sense: rereread it and fix it so the condition you want is clearly stated. Since $\mathbf Q$ is countable its algebraic closure is countable. But $\mathbf Q_p$ is uncountable. Therefore just by cardinality considerations, some (in fact most) elements of $\mathbf Q_p$ are not algebraic over $\mathbf Q$. | |
| Mar 10, 2020 at 4:22 | history | asked | user267839 | CC BY-SA 4.0 |