Timeline for Geometric meaning of small extensions ?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2011 at 17:57 | vote | accept | Qfwfq | ||
| Jan 28, 2011 at 16:45 | answer | added | user332 | timeline score: 6 | |
| Jan 28, 2011 at 14:01 | history | edited | Qfwfq | CC BY-SA 2.5 |
added 70 characters in body
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| Jan 28, 2011 at 6:23 | comment | added | Dan Petersen | This is a nice question, I think. Here is a counterexample in the other direction: consider $A = k[x,y]/(x^2,y^2)$ and $B=k[x,y]/(x^3,y^2)$. This is not a small extension since $x^2y$ is a nontrivial element of $\mathfrak{m}_B\cdot I$, but no new "direction" is added. | |
| Jan 27, 2011 at 22:57 | comment | added | Qfwfq | @Mattia: you're definitely right. The usual extension to $k[\epsilon]$ is small and it adds a "direction"... | |
| Jan 27, 2011 at 19:36 | comment | added | Mattia Talpo | I think extensions do add "directions", think about the extension $k[\epsilon]\to k$. $k$ is just the point, $k[\epsilon]$ is a point with a tangent vector.. | |
| Jan 27, 2011 at 18:56 | answer | added | Francesco Polizzi | timeline score: 5 | |
| Jan 27, 2011 at 17:23 | comment | added | Tom Leinster | I wouldn't call this a soft question! Fat, maybe... | |
| Jan 27, 2011 at 17:12 | history | asked | Qfwfq | CC BY-SA 2.5 |