The Stacks project

LaTeX: \Spec

	Introduced the macro

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

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

End conversion of etale to \'etale.

Morphisms of Spaces: Uniform latex labels for lemmas

	Only coding changes, except for moving a lemma in
	spaces-descent.tex to its proper place.

Morphisms of Spaces: Uniform latex labels for lemmas

	Only coding changes, except for moving a lemma in
	spaces-descent.tex to its proper place.

Morphisms of Spaces: properties are Zariski local on target

	Also added: types of coverings in Topologies of Spaces

Morphisms of Spaces: Relative conditions

	Trying to understand the relative versions of the local
	conditions found in Properties of Spaces

	Todo:
		Fix currently unfinished discussion of the above
		Add lemma about algebraic spaces etale over fields
		When does an algebraic space satisfy the sheaf
			condition for fpqc-coverings? This is missing in
			the discussion of algebraic space in the
			introductory chapter on algebraic spaces, but it
			doesn't have a high priority.
		Add remark discussing informally the relative conditions
			and what to do with them.

Morphisms of Spaces: Relative conditions

	Trying to understand the relative versions of the local
	conditions found in Properties of Spaces

	Todo:
		Fix currently unfinished discussion of the above
		Add lemma about algebraic spaces etale over fields
		When does an algebraic space satisfy the sheaf
			condition for fpqc-coverings? This is missing in
			the discussion of algebraic space in the
			introductory chapter on algebraic spaces, but it
			doesn't have a high priority.
		Add remark discussing informally the relative conditions
			and what to do with them.

Morphisms of Spaces: more on separation axioms

Morphisms of Spaces: Valuative criterion universal closednedd

	Finally, we have the other direction. We still have to
	reformulate this later for morphisms which are, say,
	quasi-separated.