The Stacks project

Improve various lemmas on coh of F/f^nF

Hopefully this is actually improving the readability

LaTeX

Added a new macro

\def\Im{\text{Im}}

and replaced all occurrences of \text{Im} by \Im

Whitespace changes

Tags: Added new tags

Producing K-injective resolutions

	Suppose you admit the existence of K-injective resolutions in
	the category of O-modules on a site. Next, suppose you have a
	morphism f of ringed sites and a complex K^* on the source of f
	whose cohomology sheaves are each acyclic for f_*. Then it
	doesn't seem clear to me that R^if_*K^* is just the pushforward
	of the ith cohomology sheaf of K^*. In fact I would bet this is
	wrong in general. (Any example or counter argument welcome.)

	To see what happens we add a lemma that tells you explicitly how
	to compute a K-injective resolution of a complex where now we
	assume that each of the cohomology sheaves has bounded
	cohomological dimension on sufficiently many objects of the
	site.