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assigned tag 0DTC 2017-05-20 b3e6eaa
Tags: added new tags
changed the label to lemma-splitting 2017-05-14 3a25b9c
Add correct version of the splitting lemma

Strangely this was missing...
changed the statement and the proof 2017-05-14 3a25b9c
Add correct version of the splitting lemma

Strangely this was missing...
changed the proof 2015-03-12 da6468e
amalg and coprod
changed the statement and the proof 2011-08-10 65ce54f
LaTeX: \Spec

	Introduced the macro

	\def\Spec{\mathop{\rm Spec}}

	and changed all the occurences of \text{Spec} into \Spec.
changed the statement and the proof 2010-10-09 2b090dd
End conversion of etale to \'etale.
changed the label to lemma-splitting-general 2010-06-08 8015297
Variants of splitting lemma

	Sometimes you get schemes...
changed the statement and the proof 2010-06-08 8015297
Variants of splitting lemma

	Sometimes you get schemes...
changed the statement and the proof 2010-06-08 286fd32
Proof of Lemma Tag 03FM

	Finally! Works exactly as David Rydh explained in his comments
	on the blog.
changed the statement 2010-06-07 d50ae4e
Finite part groupoid: Start
changed the statement 2010-06-07 c234af6
Formal definition of splitting of groupoid

	From the paper by Keel and Mori.

	We currently do not have enough material in the section on
	morphisms of algebraic spaces to even say what it means for a
	morphism of algebraic spaces to be quasi-finite at a point. Of
	course it is crystal clear how to define this -- but as usual it
	takes a lot of lines of tex to define it precisely, and have it
	be exactly right.
moved the statement to file spaces-more-groupoids.tex 2010-06-04 1aa1032
Start fixing etale localization

	Moved the Keel-Mori lemma to More on Groupoids in Spaces.

	Fixed the first (much easier) lemma on etale localization of
	groupoids quasi-finite over a base. The error was from not
	thinking straight about arrows in a groupoid category. This
	first lemma is used in the chapter on morphisms of algebraic
	spaces to prove that an algebraic space separated and locally
	quasi-finite over a scheme is a scheme. Hence this lemma cannot
	be moved to More on Groupoids of Spaces, because it is used
	earlier.
moved the statement to file more-groupoids.tex 2010-05-14 753a2b1
Groupoids: Put advanced material on groupoids in separated chapter

	We will rewrite the technical lemmas, the slicing lemma, and
	etale localization lemmas in order to fix errors and for
	clarity.
changed the proof 2010-05-14 753a2b1
Groupoids: Put advanced material on groupoids in separated chapter

	We will rewrite the technical lemmas, the slicing lemma, and
	etale localization lemmas in order to fix errors and for
	clarity.
changed the statement and the proof 2010-02-02 8e006a3
Groupoids: Error in proof one of the etale localization lemmas

	This has to be fixed before continuing the discussion in
	bootstrap. We can always take the formulation of this lemma from
	Keel and Mori, but it still seems possible a slightly more
	general result holds.
changed the proof 2009-10-16 b6077d7
Groupoids: Fix proof of Keel-Mori result on splitting groupoids

Signed-off-by: Aise Johan de Jong -- Strider <aise.johan.de.jong@gmail.com>
assigned tag 0DTC 2009-10-13 c539166
Tags: new tags added

	modified:   tags/tags
created statement with label lemma-quasi-finite-groupoid in groupoids.tex 2009-10-13 d6c735d
Groupoids: Etale localization of groupoids

	This is fun, since we actually have a good theory of etale
	localization of schemes, and it more or less automatically gives
	good results for etale localization of (quasi-finite) groupoids

	modified:   groupoids.tex