History of tag 03J6
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changed the proof
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2020-11-16 |
db61e94 |
Improve lemma slightly
Thanks to Zhenhua Wu
https://stacks.math.columbia.edu/tag/03GN#comment-5540
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changed the proof
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2020-11-16 |
c3cb5e7 |
Missing \dim_k inserted 3x
Thanks to Michael
https://stacks.math.columbia.edu/tag/03J6#comment-5538
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changed the proof
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2011-08-10 |
65ce54f |
LaTeX: \Spec
Introduced the macro
\def\Spec{\mathop{\rm Spec}}
and changed all the occurences of \text{Spec} into \Spec.
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changed the statement
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2009-12-23 |
2f54d62 |
Morphisms of Spaces: Bootstrap, second version
OK, so now the proof is complete. Of course the chapter on
morphisms on algebraic spaces has a curious selection of topics
at the moment, since we've tried to work towards the bootstrap
theorem, and have not developped in a straightforward way. For
example, we have at this point defined what an etale morphism of
algebraic spaces is, but not what a morphism of finite
presentation is!
This will be fixed over time.
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assigned tag 03J6
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2009-11-08 |
65620d4
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Tags: New tags added
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changed the statement
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2009-11-08 |
e545e01 |
Properties of Spaces: Split out arguments on points of spaces
The purpose of this commit is to work out in more detail the
arguments that lead to the result that a reasonable algebraic
space X has a sober space of points |X|.
In this reworking we discover the notion of an ``almost
reasonable space''. An algebraic space X is almost reasonable if
for every affine scheme U and etale morphism U --> X the fibres
of U --> X are universally bounded.
Later we will encouter the following question: Suppose given a
fibre square diagram
X' --> X
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v V
V' --> V
with V' --> V a surjective etale morphism of affine schemes,
such that X' is reasonable. Is X reasonable? If you know how to
(dis)prove this then please email stacks.project@gmail.com
Anyway, the corresponding result for ``almost reasonable''
spaces is easy. Moreover, an almost reasonable space is a
colimit of quasi-separated algebraic spaces.
But on the other hand, we do not know how to prove that an
almost reasonable space X has an open dense subspace which is a
scheme, nor do we know how to prove that |X| is sober.
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created statement with label lemma-composition-universally-bounded in morphisms.tex
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2009-11-06 |
ee1bc94 |
Morphisms: Morphisms with universally bounded fibres
Is there a more suitable name for this property? If so, please
email stacks.project@gmail.com.
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