History of tag 03IC
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changed the statement
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2013-08-03 |
6cc7a5d |
ell check: words starting with s, t, S, or T
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moved the statement to file obsolete.tex
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2012-05-16 |
7e05565 |
Improve chapter on decent spaces
A collection of things: get rid of the very reasonable material.
This is possible because we can now prove everything for
reasoble spaces which was previously only proved for very
reasonable spaces.
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moved the statement to file decent-spaces.tex
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2011-06-10 |
52c6ad3 |
Decent Algebraic Spaces
Created a new chapter "Decent Algebraic Spaces" and moved most
of the material on local conditions of algebraic spaces in
there. In the next few commits we will fix the breakage that this
causes.
The reason for the move is that this material is difficult to
understand for the beginner and that most of the other material
in Properties of Spaces and Morphisms of Spaces is easier and
more analogous to what happens for schemes.
An added advantage is that we can use results on morphisms of
algebraic spaces in the new chapter, hence it becomes easier to
develop the theory of decent spaces.
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changed the label to remark-very-reasonable-Zariski-locally-quasi-separated
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2010-01-31 |
1642b95 |
Terminology changes:
"reasonable" ---> "very reasonable"
"almost reasonable" ---> "reasonable"
David Rydh suggested this change since the notion of being (what
is now called) very reasonable is not a particularly good
notion. On the other hand the notion of being (what is now
called) reasonable behaves quite well in various situations, and
it seems hard to envision results that use the assumption of
being very reasonable that do not hold for reasonable spaces.
Still, currently there are still some results of this form, so
we need to keep the notion "very reasonable" around (of course
we will always keep it around for the sake of referencing, but
in the future we may delegate it to a forgotten corner).
TODO (soon): Introduce decent spaces. These will be
characterized by having property (gamma).
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changed the statement
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2010-01-31 |
1642b95 |
Terminology changes:
"reasonable" ---> "very reasonable"
"almost reasonable" ---> "reasonable"
David Rydh suggested this change since the notion of being (what
is now called) very reasonable is not a particularly good
notion. On the other hand the notion of being (what is now
called) reasonable behaves quite well in various situations, and
it seems hard to envision results that use the assumption of
being very reasonable that do not hold for reasonable spaces.
Still, currently there are still some results of this form, so
we need to keep the notion "very reasonable" around (of course
we will always keep it around for the sake of referencing, but
in the future we may delegate it to a forgotten corner).
TODO (soon): Introduce decent spaces. These will be
characterized by having property (gamma).
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assigned tag 03IC
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2009-10-25 |
2ad4800
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Tags: New tags added and two fixed
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created statement with label remark-reasonable-Zariski-locally-quasi-separated in spaces-properties.tex
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2009-10-21 |
a28142d |
Properties of Spaces
We started to work out the suggestion in commit 2100745. In fact
the suggestion was wrong and the correct notion is to require
that there exists a surjective etale morphism \coprod U_i --> X
such that for each i the two projection morphisms
U_i \times_X U_i --> U_i
are quasi-compact. We are calling such an algebraic space
``reasonable''. If you do not like this please complain soon.
Sofar the only interesting observation is that points on
reasonable spaces are represented by monomorphisms from spectra
of fields. We also expect that valuative criteria will work well
for reasonable algebraic spaces.
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