The Stacks project

LaTeX

Added a new macro

\def\Im{\text{Im}}

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

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

and replace all occurrences of \text{Ker} with \Ker

First macro of the project

	This gets rid of all the \nolimits commands following \lim by
	defining

	\def\lim{\mathop{\rm lim}\nolimits}

	in the file preamble.tex. As far as I can tell this is
	equivalent to \lim\nolimits where \lim is the internal command
	of TeX. The dvi files produced before and after this commit are
	identical.

LaTeX: fix lim

	Replaced all the occurences of \text{lim} by \lim or
	\lim\nolimits depending on whether the invocation occured in
	display math or not.

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.