Timeline for Is there a way to define Hecke operators "inherently" as certain endomorphisms of the Jacobian?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| S Oct 30 at 7:15 | history | suggested | Viktor Vaughn | CC BY-SA 4.0 |
Fix LaTeX expressions
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| Oct 30 at 3:58 | review | Suggested edits | |||
| S Oct 30 at 7:15 | |||||
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Nov 20, 2010 at 19:10 | comment | added | William Stein | Additional remark: I just carefully reread Section 1 of Serre-Tate (Good Reduction of Abelian Varieties), and that makes everything crystal clear. | |
| Nov 20, 2010 at 18:17 | comment | added | William Stein | Brian -- thanks for clarifying Pete's argument, which is definitely backwards. | |
| Aug 19, 2010 at 16:41 | comment | added | BCnrd | Pete, your suggested argument sounds a bit puzzling, insofar as you're not mentioning the most crucial part, which is the role of finite etale torsion levels which are fiberwise "schematically dense" and provide a bridge between the two fibers. That is, in your 3rd line it seems like you should have said "special fiber", not "generic fiber", and then you need to haul out the finite etale torsion levels to promote that to vanishing on the generic fiber, etc. (The example of $[p]$ on an elliptic curve with additive reduction shows the necessity of using finite etale torsion.) | |
| Aug 19, 2010 at 3:05 | comment | added | Pete L. Clark | WS: Yes, the reduction map always induces an injection on the endomorphism ring. This can be seen, for instance, by thinking about the Neron models: if the map were not injective, there would be a nonzero endomorphism which agrees on the generic fiber with the zero endomorphism, contradicting density of the generic fiber. | |
| Aug 19, 2010 at 1:00 | history | answered | William Stein | CC BY-SA 2.5 |