The Stacks project

Normal and reduced goes up

Skeleton section on extensions of valuation rings

Spell checking algebra.tex

Whitespace changes

LaTeX: fix colim

	Introduced the macro

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

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

Added new tags

	modified:   tags/tags

More algebra added:

	Ascent of normality along smooth ring maps
	Descent of normality along faithfully flat ring maps

	Introduced normal schemes

	modified:   algebra.tex
	modified:   properties.tex

Finally finished proof that Nagata rings are universally Japanese

	modified:   algebra.tex
	modified:   my.bib

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

Starting to write more algebra:
	Transcendence degree of field extensions
	Separability of field extensions
	Modified section on base change of algebras over fields
	Formal smoothness for extensions of fields
	Cohen rings
	Cohen structure theorem
	Nagata rings
	Japanese rings
	Ascent of normality

	modified:   algebra.tex