Timeline for de jong's alteration theorem for families
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2011 at 22:43 | vote | accept | Dmitry Vaintrob | ||
| Jul 30, 2011 at 21:17 | comment | added | Qing Liu | See however Abramovich and Karu: Weak semistable reduction in characteristic 0. Invent. Math. 139 (2000). | |
| Jul 30, 2011 at 21:07 | comment | added | Qing Liu | For higher dimension $S$, a semi-stable alteration $X'/S'$ exists if $X/S$ have relative dimension $1$. Otherwise what de Jong proves in this Ann. Fourier paper is weaker then semi-stability. I don't known whether a counterexample to semi-stable alteration exists. | |
| Jul 30, 2011 at 21:04 | history | edited | Qing Liu | CC BY-SA 3.0 |
added 91 characters in body
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| Jul 30, 2011 at 14:36 | comment | added | Dmitry Vaintrob | Thanks! I didn't see his Theorem 5.9. Is it kosher on MO to accept an answer and rewrite an edited version of a question? Qing, you're right that I'd like $S'\to S$ to be surjective (and not necessarily smooth), and it's enough for $X'/S'$ to be semistable rather than smooth. This is more like Theorem 6.5 in dJ's original paper, and for this the general case is equivalent to the $S$ local one. Is there a counterexample with some $S$ some higher-dimensional local ring? | |
| Jul 30, 2011 at 13:46 | history | answered | Qing Liu | CC BY-SA 3.0 |