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The Stacks project

History of tag 05XQ

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type time link
changed the proof 2022-01-23 9cee969
Try to use L/K notation for field extensions

We could also try to consistenly use "field extension" and not just
"extension" and consistently use "ring extension", etc.
changed the proof 2011-06-17 1692461
Neurotic changes
changed the proof 2011-03-07 9b63d1b
Two algebraicity results

	(1) The finite locally free morphisms of degree d form an
	algebraic stack called the finite Hilbert stack of the point,
	and
	(2) Res_{Z/B}(X) is an algebraic space whenever Z ---> B is
	finite locally free and X ---> Z is an algebraic space. This is
	actually a really trivial consequence of the fact that
		Mor_B(Z, X)
	is an algebraic space (see previous commit).
changed the statement and the proof 2011-03-07 f5208b9
Hom-sheaf

	Our first result is that Mor_B(Z, X) is an algebraic space if Z
	is finite locally free over the base B.
assigned tag 05XQ 2011-03-05 4d3d15e
Added two new chapters

	Of course these are virtually empty at this point. The idea of
	the chapter "criteria" is to put there the stuff which allows
	you to prove that a given stack in groupoids is an algebraic
	stack. The idea of the chapter "quot" is to put there existence
	results for Quot and Hilbert schemes/spaces.
created statement with label lemma-surjection-space-of-sections in criteria.tex 2011-03-05 ac2750e
Towards existence of finite Hilbert stacks

	Basically this lemma allows us to do \'etale localization in
	order to prove existence in ``good'' cases.