Timeline for Local coordinate system under finite integral extension
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 16, 2011 at 17:35 | vote | accept | Jesko Hüttenhain | ||
| Aug 16, 2011 at 17:35 | comment | added | Jesko Hüttenhain | Yes that's what I thought, I hadn't realized the source of my problem at that point. I guess I have to re-think this whole thing, thanks everybody. | |
| Aug 16, 2011 at 16:32 | comment | added | Graham Leuschke | The assumption on dimension is automatic from integrality, but not helpful anyway, as David points out. | |
| Aug 16, 2011 at 15:02 | comment | added | David E Speyer | You never showed (and it isn't true) that $\mathfrak{a}$ is prime. | |
| Aug 16, 2011 at 14:27 | comment | added | Jesko Hüttenhain | Hm. Yea that sounds about right? Where does my argument fail? | |
| Aug 16, 2011 at 13:51 | comment | added | David E Speyer | Look at Karl's example. $\mathfrak{q}_1$ is $\langle x^2-y^3 \rangle$, $\mathfrak{q}_2$ is $\langle y \rangle$ so $\mathfrak{a}$ is $\langle x^2-y^3, y \rangle = \langle x^2, y\rangle$, which is not maximal. | |
| Aug 16, 2011 at 13:35 | history | edited | Jesko Hüttenhain | CC BY-SA 3.0 |
added 31 characters in body
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| Aug 16, 2011 at 13:35 | comment | added | Jesko Hüttenhain | $\mathfrak{q}_i$ lies over $(x_i)$, so $\mathfrak{a}:=\sum_i\mathfrak{q}_i$ lies over $\mathfrak{m}$, so by going-up, we know $\dim(\mathfrak{a})=\dim(\mathfrak{m})$. Hence, $\mathfrak{a}$ must be maximal. Oh shoot. Do I need to require that $A$ and $B$ have the same dimension? Maybe I will just add it. | |
| Aug 16, 2011 at 12:54 | comment | added | Graham Leuschke | I don't understand the "By going up..." part. Doesn't Karl's example show that the sum of the $\mathfrak{q}$'s need not be maximal? | |
| Aug 16, 2011 at 11:40 | history | edited | Jesko Hüttenhain | CC BY-SA 3.0 |
fixed a typo
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| Aug 16, 2011 at 11:22 | answer | added | Karl Schwede | timeline score: 3 | |
| Aug 16, 2011 at 10:07 | history | asked | Jesko Hüttenhain | CC BY-SA 3.0 |