The Stacks project

Tags: Added new tags

More precision on universal homeomorphsms (rings)

Also a bit more general material on decomposition groups, etc.

More precision on universal homeomorphsms (rings)

Also a bit more general material on decomposition groups, etc.

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

and replace all occurrences of \text{Ker} with \Ker

Fix idiotic error

A counter example to the lemma as stated originally was any finite field
extension! I win a Stacks project mug!

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

LaTeX: \Spec

	Introduced the macro

	\def\Spec{\mathop{\rm Spec}}

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

Fix algebra lemma

	The lemma wasn't wrong per se, but references pointing to it
	expected more than stated.

	Note the following counter example. Suppose that k is an
	infinite field algebraic over F_p but not algebraically closed.
	Consider the ring map k ---> k' = \overline{k} of k into its
	algebraic closure. Note that for every x in k' there exists an
	integer n > 0 such that x^n is an element of k! It is true that
	the morphism of spectra is a homeomorphism, but this is not a
	universal homeomorphism!

Groupoids: Started writing about finite flat groupoids

	Immediate goal: help prove facts on points of algebraic spaces
	More gloabl goal: towards finite flat quotients in category of
		algebraic spaces

	modified:   algebra.tex
	modified:   groupoids.tex
	modified:   spaces.tex
	modified:   tags/tags

Started tags infrastructure

	new file:   scripts/add_tags.py
	modified:   scripts/functions.py
	new file:   tags/initial_tags
	new file:   tags/tags

Starting with varieties.tex

	modified:   algebra.tex
	modified:   properties.tex
	modified:   topology.tex
	new file:   varieties.tex