The Stacks project

Fix an impossible notation

Thanks to  Manolis Tsakiris
https://stacks.math.columbia.edu/tag/04GN#comment-8576

Fix and shorten a proof

Thanks to Tim Holzschuh
https://stacks.math.columbia.edu/tag/04GN#comment-4660

Remove use prime avoidance

Thanks to fherzig
https://stacks.math.columbia.edu/tag/0BSK#comment-4167

Clarify construction (strict) henselization

Thanks to Minseon Shin who writes:

"I have a question regarding the henselization
construction Tag 04GN, in the argument showing that the
category of pairs (S,\mathfrak{q}) satisfies condition
(3) (i.e. has coequalizers) in the definition of a
filtered category (002V). In order to show that
R \to S'' is etale, isn't it necessary to use at some
point the fact that etale morphisms satisfy the
cancellation property 00U7? Looking at the diagram, it
seems we need to know that \varphi, \psi, and the
diagonal S' \otimes_{R} S' \to S' are etale.

I thought this was worth pointing out since this part
seems to be what fails when we attempt the same
construction for "etale" replaced by "finitely presented
flat" (i.e. to construct the "fppf stalk" of a local
ring)."

Reorganize material henselization

OK, I still dislike henselization but it seems to be a necessary evil.

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

Cohomology and base change, IV

This time for algebraic spaces.

LaTeX: fix colim

	Introduced the macro

	\def\colim{\mathop{\rm colim}\nolimits}

	and changed all the occurences of \text{colim} into \colim.

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

Tags: added new tags

Algebra: Functoriality henselizations

Algebra: Henselian rings

	This is somewhat repetitive since we already have the analogues
	of all these results in terms of finding open neighbourhoods,
	etc. But the translation between different formulations is not
	seamless, and not automatic.