The Stacks project

Fix missing .

Thanks to Peng Du
https://stacks.math.columbia.edu/tag/05EB#comment-8387

Expand the section on local cohomology

The previous version of this section was written for the application of
it in the chapter on the pro-etale site. Hence the point of view was to
stress how one can compute the derived functor R\Gamma_I of taking
I-power torsion over Noetherian rings, by the extended alternating Cech
complex.

However, for the general development, taking the approach with the
alternating Cech complex is the correct one, because it gives us the
right adjoint R\Gamma_Z to the inclusion functor

D_{I-power torsion}(A) --------> D(A)

which we don't get by taking R\Gamma_I. Moreover, we match R\Gamma_Z
with taking cohomology supported in Z on the corresponding affine
scheme.

Tags: Added new tags

Formal glueing

	Bhargav Bhatt submitted a write up on formal glueing that I
	edited to make it fit better with the stacks project. The
	statement implies for example the following: Suppose that C is a
	smooth curve over a field k and p a closed point of C. Then
	vector bundles over C are the same thing as triples (E, E', phi)
	where E is a vector bundle on C - {p}, E' is a vector bundle on
	the formal completion of C at p, and phi is an isomorphism
	between E and E' over the punctured formal completion of C at
	p. This is sometimes a good way to think about vector bundles
	(e.g. because the vectorbundle E is trivial if it has trivial
	determinant).

	Adding this caused me to start a new chapter on algebra called
	"More on Algebra". If you have a less prosaic title, then drop
	me an email.