The Stacks project

Try to use L/K notation for field extensions

We could also try to consistenly use "field extension" and not just
"extension" and consistently use "ring extension", etc.

Fix two complaints parse.py

	One line over 80 characters and two renamed labels.

Move result from varieties into the algebra chapter

	Suggestion by Matthieu Romagny

geom. reduced algebras / schemes

	A k-algebra A is reduced if and only if its base change to
	k^{1/p} is reduced.

Small change

	Thanks to Abolfazl for pointing out "This clearly implies..."
	wasn't terribly clear (and using "clearly" is something that
	should be avoided anyway).

	Statistics:
		"clearly" occurs 356 times
		" clear " occurs 570 times
		"easy" occurs 185 times
		"omit" occurs 951 times
	So it is easy to find spots where to start improving the stacks
	project...

Varieties: Loos ends

	There is much more work to be done here. For example this
	commit adds the fact that if X is a variety over a field k then
	there exists a finite purely inseparable extension k' of k such
	that (X_{k'})_{red} is geometrically reduced -- and of course in
	actuality the result is slightly more general.

	There is a similar result regarding geometric irreducibility
	which we should add as well, and we can also think about the
	correct formulation of such a result for geometric connectivity.

	Also, in the section on unit groups we have not yet stated the
	consequence that if X is a variety over k and k is algebraically
	closed in k(X) then O(X)^*/k^* is a finitely generated abelian
	group. In particular, this gives the same result for
	geometrically integral varieties.

Added new tags

	modified:   tags/tags

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