The Stacks project

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

and replace all occurrences of \text{Ker} with \Ker

More examples of pure modules

	In particular it turns out that if we have R ---> S and N an
	S-module which is countably generated and Mittag-Leffler as an
	R-module, then it is pure relative to S/R. This finally puts a
	direct link between purity and the Mittag-Leffler condition
	which I was looking for.

	Note that there is an example that shows that one cannot go the
	other way. Namely, there exist pure modules over S/R (even when
	everything of finite type and Noetherian) which are not
	Mittag-Leffler.

Remove finite type hypothesis

	In some sense this is a simplification.

More on purity

Tags: Added new tags

First projectivity result

	as stated this lemma can be used to proceed by Noetherian
	induction on the base in certain situations.

Fixing references, etc

	Fallout from moving stuff in the previous commit.

Moving results

	Moved some esoteric results on Mittag-Leffler modules and
	completion into flat.tex apart from a result on lifting
	projective modules which I put into a section on projective
	modules.

More on Mittag-Leffler modules