The Stacks project

fix small typos

Typo in etale-cohomology

THanks to Matthieu Rommagny
https://stacks.math.columbia.edu/tag/04I7#comment-5017

Spell check: words starting with b, c, B, or C

LaTeX: \etale

Introduced the macro

\def\etale{{\acute{e}tale}}

and replaced all occurences of \acute{e}tale by \etale

Whitespace changes

LaTeX: \Sh

	Introduced the macro

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

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

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

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

Neurotic changes

	Fix (almost all) complaints of parse.py

Begin translating etale to \'etale or \acute{e}tale (in Math mode).

Uniqueness of recovering morphisms

	In Etale Cohomology and in Properties of Spaces we added lemmas
	stating that if a, b : X ---> Y are morphisms of schemes or
	algebraic spaces and if the associated morphisms of ringed topoi
	are isomorphic then a = b. This trivial result is made difficult
	to prove only because it is so damn confusing to work out
	exactly what it means!

Relocalizing morphisms of (ringed) topoi

	There is quite a bit of duplication here, but it seems
	convenient to be able to talk about this both when given
	explicit sites defining the topoi and when you are just given an
	abstract morphism of (ringed) topoi.

Etale Cohomology: Functoriality etale topoi done

	This commit puts in the last bits for the proof that a morphism
	of locally ringed topoi

		(X_{etale}, O_X) ---> (Y_{etale}, O_Y)

	always comes from a morphism of schemes X ---> Y.

	The current proof by glueing is not really that nice since it
	requires a lot of sophistication from the reader. On the other
	hand it is more or less clear that you can do this as soon as
	you start thinking about it, and in fact it is probably the
	proof that a less sophisticated mathematicien (such as me) would
	come up with in the first place. Hah!

Modules on Sites: Localization of morphisms of locally ringed topoi

	Arrggghhhh! Oh well, it is very nice how it all fits together.

Tags: added new tags

Sites: Localizing morphisms of topoi

	Realized this was missing whilst working out details on
	functoriality of small etale topoi.

Etale Cohomology: Functoriality small etale sites

	Almost done with this.