Timeline for Maximal p-extension and pro-p extension
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2023 at 17:14 | history | edited | Rellw | CC BY-SA 4.0 |
added 10 characters in body
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| Nov 14, 2023 at 15:43 | comment | added | Rellw | Thanks very much for Chris and David's useful comments! | |
| Nov 10, 2023 at 17:42 | comment | added | David Loeffler | The $p$-adic, $T$-adic, and $(p, T)$-adic topologies on $\Lambda$ are all different. For most purposes it is the $(p, T)$-adic one which is important (since it is the compact one); the other two topologies are less useful. | |
| Nov 10, 2023 at 13:08 | comment | added | Chris Wuthrich | Q_1, if I understood correctly, is just a rant that we write "maximal abelian $p$-extension of $F_{\infty}$" when you would write "maximal abelian pro-$p$-extension of $F_{\infty}$". You are right that it may be infinite. Its Galois group is the limit of the $p$-primary subgroups of the class groups of $F_n$, not the full class group. - Ultimately, it is just a question of terminology and harmless, if it is infinite there wouldn't be a maximal finite abelian $p$-extension of $F_{\infty}$. - The same applies to a $F$ itself and that answers Q2. | |
| Nov 10, 2023 at 11:43 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| S Nov 10, 2023 at 11:06 | review | First questions | |||
| Nov 10, 2023 at 15:24 | |||||
| S Nov 10, 2023 at 11:06 | history | asked | Rellw | CC BY-SA 4.0 |