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changed the statement 2015-04-01 5414f65
Fix wording in decent-spaces.tex

Thanks to Pieter Belmans
http://stacks.math.columbia.edu/tag/03ID#comment-1361
changed the label to example-not-decent 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.
changed the statement 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.
changed the statement 2011-06-15 0825897
Big set of changes

	Most of this is geared towards proving (in the "correct" way)
	that an algebraic stack is a gerbe if and only if the inertia is
	flat and locally of finite presentation over it.

	Other additions are:
		stackification and inertia
		[U/G] ---> U/G in the case of free actions
		residual gerbes are gerbes (not nec over a point!)
		presentations of inertia stacks
		definition free action
		U ---> U/R is flat + lfp in final bootstrap theorem
changed the statement 2011-06-12 b88197a
Finished cleanup decent-space.tex

	Last edit to this chapter for now.
moved the statement to file decent-spaces.tex 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.
changed the label to example-not-very-reasonable 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).
changed the statement 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).
assigned tag 03ID 2009-10-25 2ad4800
Tags: New tags added and two fixed
created statement with label example-not-reasonable in spaces-properties.tex 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.