The Stacks project

Flattening by blowing up

Still a bit rough, but the arguments are all there.
A fun lemma is that the problem is etale local on the base.
The rest is exactly as in Raynaud-Gruson (the lemma may
be there too, I'm not sure).

zerodivisor and nonzerodivisor

	Seems better this way.

LaTeX: \Spec

	Introduced the macro

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

	and changed all the occurences of \text{Spec} into \Spec.

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.

Tags: Added new tags

Lemmas on universally injective maps

	will be continued...