Timeline for Is there a relative version of Artin's approximation theorem?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2014 at 12:55 | comment | added | D.-C. Cisinski | You might want to have look at Corollary 5.4 in this paper: J. Wildeshaus, The boundary motive: definition and basic properties, Compositio Math. 142 (2006), 631-656 (also available as arXiv:math/0408295). | |
| Jan 23, 2014 at 17:04 | answer | added | Jason Starr | timeline score: 1 | |
| Jan 23, 2014 at 14:58 | comment | added | user76758 | Artin's result in the case of formal completion at a point doesn't require any smoothness hypothesis. By using Popescu's generalization of Artin approximation, the proof adapts to work etale-locally on $S$ (to get a common pointed etale neighborhood when there's a common point-completion over one on $S$) if $S$ is excellent. But in the smooth case, at least Zariski-locally, can't we just take $U$ to be the fiber square of etale maps of $X$ and $Y$ to an affine space (respecting sections), avoiding Artin approximation entirely? | |
| Jan 23, 2014 at 14:28 | comment | added | Jason Starr | The global sections might cause problems. Are you allowing to base change by an 'etale cover of $S$? | |
| Jan 23, 2014 at 12:50 | review | First posts | |||
| Jan 23, 2014 at 12:55 | |||||
| Jan 23, 2014 at 12:32 | history | asked | user45908 | CC BY-SA 3.0 |