Timeline for Schematic image of a relative Cartier divisor of a fiberwise dense open
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| Jan 25, 2015 at 6:23 | comment | added | user74230 | @QuestionMark: The theta-divisor is a red herring, and can be completely ignored for the purpose of building the canonical principal polarization of the relative Pic$^0$ of such relative curves. (If you don't want projective assumptions, you have to use a bit more descent technique.) One just uses an fppf-descent generalization of the same method which is used for curves over a field in the absence of a rational point; this is explained very cleanly in Chapter 6 of Mumford's GIT book (proof of Prop. 6.9 in section 6.1, and so on). | |
| Jan 25, 2015 at 5:52 | comment | added | Question Mark | Thank you very much! I find this an extremely instructive example to keep in mind when thinking about schematic image. As for the proof in "Neron models" where this is coming from, they must then be using their previous reduction to a regular Noetherian base at this point. I don't understand though how they manage to get the $S$-flatness of $W^{g - 1}$ (or that it is a divisor). | |
| Jan 25, 2015 at 5:41 | vote | accept | Question Mark | ||
| S Jan 25, 2015 at 3:11 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Jan 25, 2015 at 3:11 | history | made wiki | Post Made Community Wiki by Jason Starr |