History of tag 07XW
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changed the proof
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2016-11-06 |
7a43b50 |
Strong formal effectiveness => openness versality
Actually not hard to prove and you only need to check on first order
thickenings.
Bhargav's example from c31011d shows that strong formal effectiveness
does not always hold. But what about strong formal effectiveness
where the thickenings are always first order (between any two, not
just between consecutive indices)? This is the only thing needed for
the argument here, so it would be nice if it was true for algebraic
stacks in general.
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assigned tag 07XW
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2012-07-03 |
3fe4cf9
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Tags: Added new tags
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created statement with label lemma-smooth-smooth in artin.tex
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2012-06-18 |
d9b1272 |
Getting smooth morphisms towards X
Openness of versality gives this to us. But you have to worry a
bit about (purely inseparable) residue field extensions, i.e.,
you have to show that the versality condition is preserved under
a bunch of reasonable operations.
Somehow Artin never seems to run into this problem. I think
because he consistently works with covers having a fixed residue
field. So yes, it is possible to avoid this...
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