The Stacks project

Fix typo in more-morphisms

THanks to nkym
https://stacks.math.columbia.edu/tag/03GV#comment-7687

Fix typo in 03GV

Thanks to Minseon Shin

Normalization and smooth base change for spaces

move a chapter and rename a chapter

	We moved the chapter "Cohomology of Algebraic Spaces" earlier so
	we can use the results earlier in the treatment of algebraic
	spaces. Also, we finally renamed the chapter "Coherent
	Cohomology" to "Cohomology of Schemes" which is better.

Stratify by degree fibre

	This works well for flat, lfp, quasi-finite morphisms.

LaTeX: \Spec

	Introduced the macro

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

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

Smooth => regular => normal

Tags: Added new tags

More on Morphisms: Improved discussion on quasi-finite morphisms

	Now we use the material on normalization (in Morphisms) which
	was not available in the first pass on the structure of
	quasi-finite separated morphisms. In particular, using the fact
	that normalization commutes with etale base change improves the
	exposition and clarifies the proof. Not only that, it also gives
	a slightly more general result, namely, we do nnot even have to
	assume the morphism is quasi-finite at all. Just finite type and
	separated.

	Future addition: It seems quite possible that given a proper f :
	X --> S with S qc+qs then the normalization of S in X is just
	the spectrum of f_*O_X and moreover the fibres of the map to
	this normalization are connected. In other words, the connected
	fibres thing holds without assuming the base is Noetherian. It
	should be possible to prove this using the results on limits of
	schemes.

	modified:   more-morphisms.tex