The Stacks project

Fix typo in algebra

THanks to Yijin Wang
https://stacks.math.columbia.edu/tag/00TH#comment-7007

Add a missing reference

THanks to WhatJiaranEatsTonight
https://stacks.math.columbia.edu/tag/031I#comment-6689

Sign error in algebra

THanks to Bogdan
https://stacks.math.columbia.edu/tag/031I#comment-4297

Why not invoke lemma 10.130.10

Thanks to Dario Weissmann for this suggestion
https://stacks.math.columbia.edu/tag/031I#comment-3216

Clarify a statement

Thanks to Peter Johnson
http://stacks.math.columbia.edu/tag/031I#comment-1808

Clarify proof of 031I

Thanks to Minseon Shin

Fix subscript on \otimes 2x

Thanks to Minseon Shin

Whitespace changes

Formal smoothness is fpqc local on the target

Added new tags

	modified:   tags/tags

Continuing adding material to algebra.tex:

	Power series ring over a Noetherian ring is Noetherian
	Integral closure commutes with localization
	Completions of Noetherian rings are Noetherian
	Taking modules of differentials commutes with colimits
	Better characterization of formally smooth ring maps
	Short exact sequence of modules differentials associated to
		formally smooth ring map
	Formal smoothness lifts along small deformations
	Bunch of lemmas with goal to characterize separable field
		extensions as formally smooth field extensions
	Cohen rings are formally smooth
	Proof of Cohen structure theorem

	modified:   algebra.tex
	modified:   spaces.tex