Timeline for Prime Decomposition in Cyclotomic Z_p-extensions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16, 2011 at 23:25 | comment | added | Keenan Kidwell | A minor thing: the subgroup Frobenius <<topologically generates>> is open (being closed and non-trivial in $\mathbf{Z}_p$, hence closed and finite index). | |
| Sep 15, 2011 at 21:18 | vote | accept | Jeff H | ||
| Sep 15, 2011 at 19:59 | comment | added | Kevin Ventullo | By the way, this need not hold for an arbitrary $\mathbb{Z}_p$-extension of a number field. For instance, suppose $K$ is a number field which has a $\mathbb{Z}_p^2$-extension $K_\infty$. Any prime $\ell$ will split completely in the fixed field of Frob$_\ell$, and the galois group of the fixed field over $K$ has $\mathbb{Z}_p$-rank at least one. | |
| Sep 15, 2011 at 8:59 | history | edited | Kevin Ventullo | CC BY-SA 3.0 |
added 10 characters in body; deleted 8 characters in body
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| Sep 15, 2011 at 4:40 | history | answered | Kevin Ventullo | CC BY-SA 3.0 |