History of tag 03Y3
Go back to the tag's page.
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changed the statement
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2024-05-16 |
a20cecb |
Insert missing s
Thanks to Simon Vortkamp
https://stacks.math.columbia.edu/tag/03XV#comment-8847
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changed the statement and the proof
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2021-05-02 |
297c5b6 |
Clarify what is needed in bootstrap theorem
Thanks to DatPham
https://stacks.math.columbia.edu/tag/03Y3#comment-6069
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changed the statement
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2011-08-11 |
f496b59 |
LaTeX: \Sch
Introduced a new macro
\def\Sch{\textit{Sch}}
and replaced all the occurences of \textit{Sch} with \Sch.
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changed the statement and the proof
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2010-10-09 |
97a5c76 |
Begin translating etale to \'etale or \acute{e}tale (in Math mode).
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changed the proof
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2010-01-27 |
a74ca1c |
More morphisms: Cohen-Macaulay morphisms
Cohen-Macaulay morphisms are fppf local on the target and
syntomic local on the source.
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moved the statement to file bootstrap.tex
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2010-01-25 |
79c5606 |
Bootstrap: Added new chapter
It seems better to discuss the bootstrap theorems in a separate
chapter following the discussion of the basic material on
algebraic spaces. This can then be used in the chapter on
algebraic stacks when discussing presentations and what not.
The goal is to prove the theorem that an fppf sheaf F for which
there exists a scheme X and a morphism f : X --> F such that
f is representable by algebraic spaces
f is flat, surjective and locally of finite presentation
is automatically an algebraic space. We have almost all the
ingredients ready except for a slicing lemma -- namely somehow
lemma 3.3 part (1) of Keel-Mori.
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changed the proof
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2010-01-25 |
79c5606 |
Bootstrap: Added new chapter
It seems better to discuss the bootstrap theorems in a separate
chapter following the discussion of the basic material on
algebraic spaces. This can then be used in the chapter on
algebraic stacks when discussing presentations and what not.
The goal is to prove the theorem that an fppf sheaf F for which
there exists a scheme X and a morphism f : X --> F such that
f is representable by algebraic spaces
f is flat, surjective and locally of finite presentation
is automatically an algebraic space. We have almost all the
ingredients ready except for a slicing lemma -- namely somehow
lemma 3.3 part (1) of Keel-Mori.
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assigned tag 03Y3
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2010-01-03 |
92b033f
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Tags: added new tags
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changed the proof
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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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created statement with label theorem-bootstrap in spaces-morphisms.tex
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2009-12-21 |
b7c3159 |
Morphisms of Spaces: Bootstrap, first version
Here we finally prove the long awaited fact that a sheaf for the
fppf topology whose diagonal is representable by algebraic
spaces, and which has an etale surjective covering by an
algebraic space, is itself an algebraic space. We deduce this
from the, itself interesting, proposition that an algebraic
space which is separated and locally quasi-finite over a scheme
is itself a scheme.
Both of these results are essential for being able to continue
to the next level, uh, I mean algebraic stacks.
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