New chapter

Filename: proetale.tex
Title: Pro-\'etale Cohomology
Preliminaries
Fix typo
Algebraic construction of w-local pro-Zariski cover
Some more topology
Stone-Cech compactification

Also one point compactification
Finish the Gleason thing completely

Using the Stone-Cech compactification to produce enough extremally
disconnected spaces.
More lemmas on spectral spaces
Constructing ind-Zariski ring maps
Refer to new topology material in algebra chapter
Characterize weakly contractible' spectral spaces

What is good terminology?
A bit more small thngs in proetale.tex
Application to ring maps identifying local rings

Later we will do similar for weakly etale ring maps.
Olivier's theorem on absolutely flat extensions of strictly henselian rings
Fix missing references and add some arguments
Weakly etale versus ind-etale

Still a bit rough.
Cleanup and an example
Construction of w-contractible covers
Fix an error

It isn't clear that a closed subset of an extremally disconnected
space is extremally disconnected -- something that was tacitly
assumed in one of the arguments.

Is there a counter example...?
Fix a lemma

The statement of lemma-w-local-algebraic-residue-field-extensions
was wrong. Fixed and now there is a proof as well.