The Stacks project

Relate pseudo-coherent morphisms to relative pseudo-coherence

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Need separated for Cech complex

	To get the Cech complex for crystalline cohomology as
	advertised we need to assume X is separated and not just that X
	has affine diagonal. Of course you can make it work when X has
	affine diagonal or even in complete generality using
	hypercoverings but not with the exact same construction. Since
	in any case crystalline cohomology is ONLY well behaved for
	proper smooth morphisms it doesn't seem like a big restriction
	to assume that X is separated. Moreover, we don't actually need
	to use the Cech complex in any of the later arguments.

	Still, it is pleasing that one can _define_ crystalline
	cohomology of a quasi-compact separated scheme using an
	alternating Cech complex and de Rham cohomology of local lifts.
	This is of course much quicker than developing all of the theory
	of crystalline cohomology...

Series of remarks on crystalline cohomology

	This is just a plan for how to work through this mess of
	crystalline cohomology. Please let me know if you have comments,
	suggestions, errors, etc.