Timeline for Elements of trace zero in a field extension
Current License: CC BY-SA 2.5
6 events
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| Jul 15, 2010 at 21:13 | vote | accept | Izhar Oppenheim | ||
| Jul 15, 2010 at 14:09 | comment | added | Charles Matthews | (Continuation) Well, if the image contains the line as a matter of geometry, it looks like the pre-image of the line will be a curve on the quadric. Typically then there will not be a $K$-point mapping to a given $K$-point, unless we're in a trivial kind of situation. Izhar, where does this come from? | |
| Jul 15, 2010 at 14:08 | comment | added | Charles Matthews | There is some geometry here. I don't see the initial motivation for the question, but here is the issue (and why I intuited the answer would be no in general). Using homogeneity, I thought the question came down to two things: does the image of a certain quadric surface in projective 4-space under a certain linear mapping contain a certain line? And given that it does, there is the rationality issue of whether there is a $K$-point mapping to a given $K$-point. (Continued) | |
| Jul 15, 2010 at 13:53 | history | edited | Pete L. Clark |
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| Jul 15, 2010 at 13:51 | answer | added | Tom Goodwillie | timeline score: 7 | |
| Jul 15, 2010 at 7:23 | history | asked | Izhar Oppenheim | CC BY-SA 2.5 |