Timeline for Are Frey elliptic curves semi-stable?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2022 at 21:02 | vote | accept | did | ||
| Jul 19, 2022 at 9:49 | comment | added | David Loeffler | I cannot resist pointing out that the question, interpreted literally, is trivial: we know that FLT is true, hence Frey curves do not exist. So the statement "all Frey curves are semistable" is vacuously true, as is the statement "all Frey curves are non-semistable". Ex falso quodlibet! (This is a facetious comment, I have nothing to add to the excellent answers already posted explaining how to prove semistability of Frey curves without using FLT.) | |
| Jul 19, 2022 at 5:02 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Jul 19, 2022 at 3:59 | history | became hot network question | |||
| Jul 18, 2022 at 20:37 | answer | added | KConrad | timeline score: 9 | |
| Jul 18, 2022 at 20:32 | comment | added | Chris Wuthrich | From the form of the equation, you see that the curve has multiplicative reduction for all odd primes as we may assume that $a$ and $b$ are coprime. So the curve is semistable at all primes except maybe $2$. This information is useful as it tells you that the level of a newform attached to the hypothetical curve is a power of $2$ times a square-free integer. Then level-lowering will bring it down to $2$ and to the contradiction. If there were a square involved in the starting level this would be harder. | |
| Jul 18, 2022 at 19:59 | history | asked | did | CC BY-SA 4.0 |