The Stacks project

Add general remark relating sheaves big/small

Fix typos

Remove a few \romannumeral commands

Thanks to Antoine Chambert-Loir
http://stacks.math.columbia.edu/tag/021K#comment-1237

Typos

Thanks to David Zureick-Brown
http://stacks.math.columbia.edu/tag/02EM#comment-31

'pull back' ----> 'pullback'

	This is a bit more tricky as we sometimes use the pull in 'pull back' as a verb.

Whitespace changes

LaTeX: get rid of useless brackets

LaTeX: \Sh

	Introduced the macro

	\def\Sh{\mathop{\textit{Sh}}\nolimits}

	and replaced all occurences of \textit{Sh} with \Sh.

LaTeX: \Ob

	Introduced a macro

	\def\Ob{\mathop{\rm Ob}\nolimits}

	and replaced any occurence of \text{Ob}( with \Ob(. There are
	still some occurences of \text{Ob} but these are sets, not the
	operator that takes the set of objects of a category.

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

	and replaced all the occurences of \textit{Sch} with \Sch.

Properties of Spaces: etale morphisms of spaces and O_X-modules

	If X --> Y is an etale morphism of algebraic spaces, then
	pullback of O-modules is exact. This is true because the
	associated morphism of topoi is a localization.

Topologies on Schemes: Fix error

	In the lemma describing sheaves F on the big etale site of X in
	terms of sheaves F_T on the small etale sites of schemes T/X you
	need to require that the transition maps

		c_f : f^{-1}(F_T) --> F_{T'}

	are isomorphisms when f is etale! This was omitted in the
	previous version.

Started tags infrastructure

	new file:   scripts/add_tags.py
	modified:   scripts/functions.py
	new file:   tags/initial_tags
	new file:   tags/tags

Done with Zariski sites for now

	modified:   topologies.tex

More about Zariski zites

	modified:   topologies.tex