The Stacks project

blow-ups, blow ups, and blowups

THis is made difficult because I can 'blow up' something

Thanks to Antoine Chambert-Loir
https://stacks.math.columbia.edu/tag/01OF#comment-2823

Use macro for Spec

Add reference to an internal lemma

Thanks to Burt Totaro

Convert \bf into \mathbf in mathmode

Hopefully this will solve some observed problems with mathjax

Tags: Added new tags

Also fixed two references

Stop parse.py from complaining too much

-- the \section{...} command had better be on one line because I am not
sure what the consequences will be for the scripts used to munge the
stacks project data if the title spans two lines. As a consequence we
now have a line in examples.tex which is more than 80 characters long.
As far as I know none of the python or php scripts actually depend on
having 80 characters per line. (I couldn't think of a suitable shorter
title of this section.)
-- We require $$ to be alone by themselves on a line.
-- Fixed a reference.

Revised chapters "Examples", "Descent", "Algebraic Spaces"

I attach a proposed revised version of the chapter "Examples"
from the Stacks Project. I added another example by Hironaka,
showing that projective morphisms do not satisfy descent
in the fpqc topology on schemes. I modified the earlier example
by Hironaka (showing that projectivity is not Zariski-local)
to match the notation in this new example.

I also attach revised versions of the chapters "Descent"
and "Algebraic Spaces", with brief links to the new example.