The Stacks project

Improve discussion connectedness in Stein factorization

Of course it doens't change much but it is a bit better this way

amalg and coprod

Upgrade to results from lemmas to propositions

Namely, Grothendieck's result on vanishing of cohomology on Noetherian
topological space and Grothendieck's result on proper pushforward of
coherent sheaves

Change definition of connected: require nonempty

Thanks to Burt Totaro

Small changes

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.

LaTeX: \Spec

	Introduced the macro

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

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

First macro of the project

	This gets rid of all the \nolimits commands following \lim by
	defining

	\def\lim{\mathop{\rm lim}\nolimits}

	in the file preamble.tex. As far as I can tell this is
	equivalent to \lim\nolimits where \lim is the internal command
	of TeX. The dvi files produced before and after this commit are
	identical.

LaTeX: fix lim

	Replaced all the occurences of \text{lim} by \lim or
	\lim\nolimits depending on whether the invocation occured in
	display math or not.

End conversion of etale to \'etale.

Tags: Added new tags

More on Morphisms: Improved readability of proof Stein factorization

	Only in the general case. Also changed designation into theorem
	from lemma.

More on Morphisms: Improved readability of proof Stein factorization

	Only in the general case. Also changed designation into theorem
	from lemma.

More on Morphisms: Stein factorization for general proer maps

	This is a little rough at the moment and needs to be cleaned up.
	The basic idea is that ytou first prove the result for closed
	subschemes of projective space over a ring and then reduce the
	general case to that by a simple application of Chow's lemma.

More on Morphisms: Stein factorization Noetherian case

	The proof of existence and properties of the Stein factorization
	in the Noetherian case is straightforward because we already
	have the theorem on formal functions and preliminary results on
	normalization, etale neighbourhoods, cohomology and base change
	and so on