Timeline for Totally ramified p-extension over $F_q((X))$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 26, 2011 at 14:13 | comment | added | Chandan Singh Dalawat | On the contrary, as the level $m$ of $D$ grows, so does the valuation $v_L({\frak{D}}_{L|K})$ of the different ${\frak{D}}_{L|K}$ of $L=K(\wp^{-1}(D))$ over $K$; by Hilbert's formula $$v_L({\frak{D}}_{L|K})=(1+m)(p-1).$$ | |
| Dec 26, 2011 at 13:56 | vote | accept | user20167 | ||
| Dec 26, 2011 at 13:54 | comment | added | user20167 | Dear Dalawat, thanks for your answer. So in this case, the different of a totally ramified p-extension can be arbitarily small, (I guess it doesn't happen in the mixed character case, say, $\mathbf{Z}_p$ ), and the smaller it becomes, (or the corresponding \textbf{level} grows?), this extension is more close to an inseparable extension? | |
| Dec 26, 2011 at 11:19 | history | edited | Chandan Singh Dalawat | CC BY-SA 3.0 |
Addendum
|
| Dec 26, 2011 at 4:22 | history | edited | Chandan Singh Dalawat | CC BY-SA 3.0 |
added 259 characters in body; added 15 characters in body
|
| Dec 26, 2011 at 4:14 | history | answered | Chandan Singh Dalawat | CC BY-SA 3.0 |