History of tag 07Z1
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assigned tag 07Z1
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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-limit-preserving-on-objects-not-limit-preserving in examples.tex
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2012-06-15 |
4121f96 |
Formulating the axioms
I've decided to formulate the axiom on effectivity as asking for
an equivalence
X(R) = lim X(R/m^n).
There are two reasons for this: (1) this is what you get when X
is an algebraic stack and (2) I don't know any case where the
natural proof of the density that Artin requires, doesn't give
you the equality as stated above. If you do know an example of
this, please let me know.
What I can imagine being easier to prove (in examples) is that
versal deformations can be approximated over complete local
rings. (For example, these complete local rings may have
additional properties which help approximate the given formal
objects.) In other words, it may make sense to have a second
version of the theorem where we assume the existence of
*effective* versal formal objects without assuming RS. And this
also makes sense as after all Artin's approximation method takes
as input such things...
To be continued.
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