diff -urN -X stacks-0.2/src/documentation/dontdiff stacks-0.2.orig/src/etale.tex stacks-0.2/src/etale.tex
--- stacks-0.2.orig/src/etale.tex	2006-03-05 03:48:21.000000000 +0000
+++ stacks-0.2/src/etale.tex	2006-03-06 02:34:06.000000000 +0000
@@ -821,11 +821,13 @@
 direction, we are told that $f$ is \'etale and universally injective. As it
 is a flat morphism of finite type, it also universally open. Hence, it is
 universally a homeomorphism onto its image. Replacing $Y$ with $f(X)$, we may
-assume that $f:X \to Y$ is a universal homeomorphism and, consequently,
-universally closed and, therefore, proper. By Zariski's main theorem and
-the unramifiedness assumption, it follows that $f$ is a finite \'etale
-covering. However, since $f$ is a homeomorphism, this covering has degree
-$1$ and, consequently, is an isomorphism. 
+assume that $f:X \to Y$ is a universal homeomorphism.  Now, if $f$ had a 
+section, the section would have to be an open immersion (because $f$ is 
+unramified) that is surjective (because $f$ is a homeomorphism). That is, it 
+would be an isomorphism and that would prove our claim. On the other hand, to 
+show that $f$ is an isomorphism, it clearly suffices to work after a faithfully 
+flat base change. But $f$ itself provides such a base change! And once we base
+change via $f$, the diagonal provides a section. The claim follows.
 \end{proof}
 
 \noindent
@@ -1014,88 +1016,6 @@
 structure theorem and the fact that the analytification commutes with the
 formation of the completed local rings -- the details are left to the reader.
 
-\section{Some pseudo-mathematical reasons to study \'etale cohomology}
-\label{section-pseudo-mathematical}
-
-\noindent
-Perhaps\footnote{What follows are imprecise ``philosophical'' reasons to
-pursue \'etale cohomology. They aren't even guaranteed to be mathematically
-correct without additional hypotheses and, consequently, should be taken with
-a pinch of salf.} the most important goal of modern algebraic geometry is to
-define the ``right'' cohomology theory in the algebraic category. What we
-mean by this is a cohomology theory which does for algebraic geometry what
-singular cohomology does for analytic geometry. As the theory of \'etale
-cohomology is an attempt to fulfill this requirement, we try to motivate
-its construction as a natural analogue of the topological one. 
-
-\smallskip\noindent
-Before we define \'etale cohomology, perhaps, a few words are in order as to
-why the standard sheaf cohomology (cohomology for the Zariski topos, or, as
-its better known, Zariski cohomology) is inadequate. First off, while Zariski
-cohomology groups of varieties are vector spaces over the field of definition
-of the variety which can possibly be of characteristic $p$, an ideal
-cohomology should have ``$\mathbf{Z}$-coefficients'' or, failing that, at least
-characteristic $0$ coefficients. Secondly, the higher cohomology groups of 
-a constant sheaf are trivial for Zariski cohomology while they carry
-incredibly refined information for singular cohomology. Lastly, we'd like a
-theory with meaningful consequences for affine varieties as well. After all,
-affine varieties are not as homogeneous as their analytic counterparts. 
-
-\smallskip\noindent
-The reason for all these failures is, of course, that the Zariski topology is
-way too coarse. Indeed, the basic open subsets of $\mathbf{C}^n$ for the Zariski
-topology are complements of hypersurfaces! A possible solution, therefore,
-could entail defining a new topology with smaller open sets. Unfortunately,
-as the crutch of analytic geometry depends heavily on metrics to define
-``small'' open subsets, it isn't exactly clear what a small open set in the
-algebraic category should constitute. However, a cute analytic fact (analytic
-geometry to the rescue again!) and the theory of Grothendieck topologies saves
-the day, as we shall shortly see. Before that, however, lets define \'etale
-cohomology.
-
-\smallskip\noindent
-With the general nonsense of Grothendieck topologies, defining \'etale
-cohomology is is a breeze. Indeed, the first step, after fixing the scheme
-$X$ whose \'etale cohomology we want to define, is to define the \'etale
-site $X_{et}$ of $X$. The underlying category of this site is the category
-of all separated \'etale $X$-schemes (all morphisms between such schemes are
-forced to be \'etale); the coverings are simply families of (necessarily
-\'etale and, therefore, open) maps whose total image is the whole space. The
-basic properties of \'etale morphisms show that this indeed defines a site.
-The category of sheaves on this site, the \'etale topos of $X$, is denoted by
-$Et(X)$. With these definitions in place, the \'etale cohomology of $X$ with
-coefficients in $\mathcal{F} \in Et(X)$ is defined as the cohomology of the
-site $X_{et}$ with coefficients in $\mathcal{F}$.
-
-\smallskip\noindent
-Next, we point out the cute (and fundamental) analytic fact that justifies
-the choice of \'etale cohomology as the correct analogue of singular
-cohomology. For an analytic space $X$, the \'etale topos
-$Et(X)$\footnote{This is defined in complete analogy with the algebraic
-construction above, with (analytic) local isomorphisms replacing the
-\'etale morphisms of algebraic geometry.} is equivalent, as a category,
-to the standard topological topos $Top(X)$ whose cohomology is, by
-definition, singular cohomology\footnote{This follows easily from the
-sheaf axioms once one observes that if $U \to X$ is a local homeomorphism
-from a topological space $U$ to an analytic space $X$, then there is a
-unique analytic structure on $U$ which makes the preceeding map an analytic
-map}. Since sheaf cohomology can be defined intriniscally in terms of the
-topos (the global sections functor can be the defined as the functor
-represented by the final object of the topos, thereby making no reference to
-the base space), singular cohomology can also be computed as the cohomology
-of the the \'etale topos. 
-
-\smallskip\noindent
-Thus, if we are to proceed by analogy with analytic geometry, all that remains
-is to formulate the right notion of a local isomorphism in the algebraic
-category. But that was precisely what we did earlier! Indeed, we have
-already given enough reasons to justify the choice of \'etale morphisms as
-the correct algebraic analogue of the local isomorphisms in analytic
-geometry. Thus, given the analytic fact mentioned above, it is at least
-reasonable to expect \'etale cohomology to be a good replacement for
-singular cohomology in the algebraic category. To see why this is actually
-the case, one must study massive volumes of incomprehensible french math.
-
 
 \smallskip\noindent
 To continue reading,