Timeline for Isomorphism on p-torsion of Neron models
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2011 at 3:04 | comment | added | Saikat Biswas | Indeed. We know that, over $U$, $\mathcal{B}^0[p]$ is quasi-finite flat and separated, and it has a finite flat subgroup scheme, say $F\mathcal{B}^0[p]$. As I mentioned, I suppose that there is a closed immersion of $F\mathcal{B}^0[p]$ into $\mathcal{A}^0[p]$ but not sure exactly why | |
| Jun 8, 2011 at 23:21 | comment | added | Kevin Buzzard | Oh -- maybe I'm misunderstanding. What is "the finite flat multiplicative type subgroup-scheme of $B^0[p]$"? Note that $B^0[p]$ is not flat. I guess it will contain as a subscheme some flat lifting of the special fibre though, which will I guess then be a closed subscheme of $A^0[p]$. Maybe that's what you're asking, in which case it sounds true to me. | |
| Jun 8, 2011 at 20:02 | comment | added | Kevin Buzzard | I don't think it can be true because the generic fibres are isomorphic and dense, so how can anything be a closed subgroup of anything? | |
| Jun 8, 2011 at 6:34 | comment | added | Saikat Biswas | Thank you for the counterexample. Having read Section 1 of Mazur's Rational Isogenies paper, I tried to work out some of the details in your counterexample and (although I'm not entirely sure I have it right) it seems that over $\mathbb{Z}_{\ell}$, there might be a closed immersion of the finite flat multiplicative type subgroup-scheme of $\mathcal{B}^0[p]$ into $\mathcal{A}^0[p]$. Is this true? | |
| Jun 5, 2011 at 8:12 | history | undeleted | Kevin Buzzard | ||
| Jun 5, 2011 at 8:12 | history | edited | Kevin Buzzard | CC BY-SA 3.0 |
added reference
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| Jun 5, 2011 at 7:57 | history | edited | Kevin Buzzard | CC BY-SA 3.0 |
put in explanation of why post was deleted
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| Jun 5, 2011 at 7:50 | history | deleted | Kevin Buzzard | ||
| Jun 5, 2011 at 7:41 | history | answered | Kevin Buzzard | CC BY-SA 3.0 |