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Oct 24, 2010 at 22:19 comment added Ben Webster I believe your argument, but it takes an input the point which is the crux of the matter for me (i.e. the barrier between me and the result I ultimately want) which is whether X^T is flat over S. I just posted a question about whether/when this is true, probably literally while you were writing your addendum.
Oct 24, 2010 at 22:09 history edited David Treumann CC BY-SA 2.5
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Oct 24, 2010 at 19:11 comment added Ben Webster In case it's relevant, the X's I have in mind have rational singularities, and in particular, are Cohen-Macaulay. It would be a real beast to try to prove that they are complete intersections, since there's no really natural choice of embedding, but something like Gorenstein or l.c.i. is more conceivable.
Oct 24, 2010 at 4:50 history answered David Treumann CC BY-SA 2.5