  Let $M$ denote a finitely generated module over a Noetherian ring $R$. For an
ideal $I \subset R$ there is a study of the endomorphisms of the local
cohomology module $H^g_I(M), g = \operatorname{grade} (I,M),$ and related
results. Another subject is the study of left derived functors of the $I$-adic
completion $\Lambda^I_i(H^g_I(M))$, motivated by a characterization of
Gorenstein rings given in the book by Simon and the author. This provides
another Cohen-Macaulay criterion. The results are illustrated by several
examples. There is also an extension to the case of homomorphisms of two
different local cohomology modules.
