The Stacks project

Algebraic stacks thickening of an algebraic space

Thanks to Matthew Emerton, Toby Gee, and Brandon Levin

Matthew writes:

"Please find attached a PDF file, and the underlying LaTeX file, giving
a proof of the following result, which I couldn't find in the stacks
project, but which might belong there:

An algebraic stack thickening of an algebraic space is again an
algebraic space

and some related results (replace ``algebraic space'' by
``Deligne--Mumford stack'', ``quasi-DM stack'', etc.).

First, apologies if this is already there, and I missed it.

Second, this write-up arose out of discussions with Brandon Levin and
Toby Gee, and reflects contributions of all three of us. Brandon also
told me that he heard of this result from Bhargav Bhatt, but didn't know
of a reference.

<--------snip--------->

It would be great if this could be incorporated into the Stack project.
I think that Toby and I might need things like this in our work at some
point, and I think maybe Brandon does as well, and having the stacks
project as a reference for it would be very convenient!

Cheers,

Matt"

LaTeX: \etale

Introduced the macro

\def\etale{{\acute{e}tale}}

and replaced all occurences of \acute{e}tale by \etale

Typo -- stacs

Thanks to David Zureick-Brown
http://stacks.math.columbia.edu/tag/075Z#comment-33

Proposition on LQC modules with flat base change

	Hopefully this proposition will make it easier to reference all
	the results on LQC+flat-b-c we have now collected together.

Use previously introduced lemma

Tags: added new tags

Tags: added new tags

Fix snafu regarding "Serre subcategories"

	Wasn't careful enough to spell out exactly what was needed to define
	the subcategory of complexes with cohomology in a subcategory. There
	does not seem to be universal agreement on what is a "thick"
	subcategory of an abelian category, so we decided to not use this
	terminology. Instead we used "weak Serre subcategory" to indicate a
	strictly full subcategory closed under kernels and cokernels.

	Let me know if you disagree with this terminology.

Move section + slight improvement

Pushforward LCQ and flat comparisons

	This is the second ingredient for a naive discussion of
	pushforward of quasi-coherent sheaves.

Pushforward LQC via qc+qs morphisms

	This is the first ingredient for a naive discussion of
	pushforward of quasi-coherent sheaves.