The Stacks project

Fix garbled language

Thanks to Matthew Emerton
http://stacks.math.columbia.edu/tag/03KI#comment-2099

LaTeX: \Spec

	Introduced the macro

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

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

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: Valuative criterion + finite separable extensions

	In the existence part of the valuative criterion for algebraic
	spaces it is enough to take a finite separable extension of the
	fraction field of the dvr. It is sometimes also necessary. It
	seems that if the morphism is separated, then it shouldn't be
	necessary, but we'll return to that later.