Timeline for Image of the norm map for degree $3$ galois extension over $\mathbb{Q}$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2018 at 20:45 | comment | added | reuns | @user300 The easiest way is to find the cyclotomic field $F$ your abelian extension $E/Q$ is contained in, then deduce the splitting of $p O_E$ and the norms $N_{E/Q}$ from $Gal(F/E)$. | |
| Sep 15, 2018 at 20:09 | comment | added | user300 | @Lubin: haha ok :) | |
| Sep 15, 2018 at 16:08 | comment | added | Lubin | As an aged mathematician with failing eyesight, I ask you to avoid using $\alpha$ and $a$ in the same equation. | |
| Sep 15, 2018 at 11:37 | comment | added | Chris Wuthrich | In this case this is just basic algebraic number theory. If you really want to understand the image of the norm map in abelian extensions, read any text on global class field theory. | |
| Sep 15, 2018 at 10:24 | vote | accept | user300 | ||
| Sep 15, 2018 at 10:21 | answer | added | S. carmeli | timeline score: 8 | |
| Sep 15, 2018 at 10:19 | comment | added | user300 | @ChrisWuthrich : Ok. Can you give me a reference for the results, you used here? Thanks. | |
| Sep 15, 2018 at 10:14 | comment | added | Chris Wuthrich | Your field $E$ in the example is $\mathbb{Q}(\mu_7)^{+}$; it has class group $1$. Primes that split are those congruent to $\pm 1$ modulo $7$. These primes, $7$, $-1$ and the cubes of all other primes will generate the image of the norm map in $\mathbb{Q}^{\times}$. For instance $a=2$ is not a norm. This can be done similar for other $E$. | |
| Sep 15, 2018 at 10:05 | review | First posts | |||
| Sep 15, 2018 at 11:29 | |||||
| Sep 15, 2018 at 10:01 | history | asked | user300 | CC BY-SA 4.0 |