The Stacks project

Rearrange material on local cohomology

Local cohomology and restriction

Fix the first FIXME in restricted.tex

Finally we have a good approach to the remark on higher Exts from an
I-power torsion module into an arbitrary module. Also, now the
treatement of the derived category of complexes with torsion cohomology
modules parallels better the treatement of derived complete complexes.

Tags: Added new tags

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.