The Stacks project

Cohomology F-crystal

	Improved exposition. Also split out the result on pullback via
	relative Frobenius morphism of a smooth scheme.

Reorganize material on complete local rings

First macro of the project

	This gets rid of all the \nolimits commands following \lim by
	defining

	\def\lim{\mathop{\rm lim}\nolimits}

	in the file preamble.tex. As far as I can tell this is
	equivalent to \lim\nolimits where \lim is the internal command
	of TeX. The dvi files produced before and after this commit are
	identical.

LaTeX: fix lim

	Replaced all the occurences of \text{lim} by \lim or
	\lim\nolimits depending on whether the invocation occured in
	display math or not.

Noetherian completions

	If R is complete wrt I and R/I is Noetherian and I is finitely
	generated, then R is Noetherian.

Structure of countably generated Mittag-Leffler modules over henselian rings

	Works exactly as predicted. We might want to split out the
	contruction of the splitting of a module given an endomorpism.

Added new tags

	modified:   tags/tags

More stuff in algebra.tex:

	Integral closure is transitive
	Surjectivity of completion of surjective maps?
	Definition of I-adically complete modules
	Criterion as to when completion is complete
	Completion complete in Noetherian case
	Finiteness criterion (still not done)
	Residue field extension of map dvrs bounded
	Complete local ring with finitely generated maximal ideal is
		Noetherian
	Lemmas on Japanese property
	Starting to prove Tate's theorem on Japaneseness of complete
		rings

	modified:   algebra.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