Timeline for Finding the inertia group
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 16, 2015 at 15:23 | vote | accept | Pablo | ||
| Aug 16, 2015 at 12:15 | answer | added | Peter Mueller | timeline score: 3 | |
| Aug 16, 2015 at 9:54 | comment | added | ABCDveve | You can use the local fields database of Jones and Roberts, or look it up in their paper (see 3.5, and 4.1 for identifying quartic types). Knowing how to compute the automorphism group helps, which is by Panayi root-finding as explained there. math.la.asu.edu/~jj/localfields hobbes.la.asu.edu/localfields/database.pdf | |
| Aug 16, 2015 at 4:20 | comment | added | Pablo | @KConrad Sadly enough no, I have just used a computer to see that it factors as a linear factor times a quartic factor in $\mathbb{Q}_2$. How do I see that it is $D_4$? | |
| Aug 16, 2015 at 4:10 | comment | added | KConrad | As a first step, have you been able to compute the Galois group of the splitting field of $h$ over $\mathbf Q_2$? I worked out that it is $D_4$ (group of symmetries of a square). | |
| Aug 15, 2015 at 23:44 | answer | added | Will Sawin | timeline score: 2 | |
| Aug 15, 2015 at 20:16 | history | asked | Pablo | CC BY-SA 3.0 |