Timeline for reduction of elliptic curves
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2013 at 1:26 | vote | accept | kiseki | ||
| Sep 11, 2012 at 9:57 | comment | added | kiseki | Thank you very much, Pof.Liu. I have found the result in your book. | |
| Sep 11, 2012 at 8:20 | comment | added | Qing Liu | continued: the morphism downstairs is also an isomorphism. If you don't want to use base change, the result can also be found in my book, Thereom 10.2.14. | |
| Sep 11, 2012 at 8:16 | comment | added | Qing Liu | @kiseki, I just check BLR's book. In Proposition 1.5/1, they state (and prove) that the smooth locus is the Néron model for elliptic curve, under the condition that the base field is strictly Henselian. In general, by Néron mapping property, the identity on the generic fiber extends to a morphism from the Néron model to the smooth locus of the minimal regular model. Base change this morphism to the strict henselization of the base ring. As both Néron and minimal regular models commute with this kind of base change, by BLR, we have an isomorphism upstair. As the base change is faithfully flat, | |
| Sep 10, 2012 at 8:01 | history | answered | Qing Liu | CC BY-SA 3.0 |