Timeline for Extending abelian schemes and their polarizations from an open subset
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 23 at 22:32 | vote | accept | TCiur | ||
| Feb 5 at 17:04 | answer | added | TCiur | timeline score: 0 | |
| Feb 2 at 11:27 | history | edited | TCiur | CC BY-SA 4.0 |
edited body
|
| Feb 2 at 9:54 | history | edited | TCiur | CC BY-SA 4.0 |
added 1410 characters in body
|
| Jan 29 at 20:57 | comment | added | TCiur | @JasonStarr But you are right, I want to know if Faltings-Chai and Vasiu-Zink have any global implications, about abelian schemes over nice schemes over $\mathbb{Z}$, as opposed to $\mathbb{Z}_{(p)}$ or $\mathbb{Q}$ | |
| Jan 29 at 20:55 | comment | added | TCiur | @JasonStarr Suppose that the hypotheses for Faltings-Chai and Vasiu-Zink hold at all stalks of the structure sheaf of $S$ (I.E. $S\backslash U$ has codimension $\geq 2$ and the indices of ramification at all stalks are $1$). Then does 'extendability' hold? Alternatively, if for any prime $p \in spec(\mathbb{Z})$, the fiber $A_{(p)} \to U_{(p)}$ above $\mathbb{Z}_{(p)}$ can be extended to an abelian scheme over all of $S_{(p)}$, does "extendability" hold? | |
| Jan 29 at 19:47 | review | Close votes | |||
| Feb 3 at 3:08 | |||||
| Jan 29 at 16:02 | comment | added | Jason Starr | I do not understand your argument above. Are you asking whether or not you can check "extendability" as a condition over the Spec of stalks of the structure sheaf of $S$? The answer to that is "yes", and that is what the Faltings-Chai and Vasiu-Zink results are about. However, you seem to be asking whether "extendability" always holds, even without assuming extendability over Spec of stalks of the structure sheaf, and the answer to that is "no." | |
| Jan 29 at 15:38 | history | edited | TCiur | CC BY-SA 4.0 |
added 43 characters in body
|
| Jan 29 at 15:24 | history | asked | TCiur | CC BY-SA 4.0 |