The Stacks project

Yet another characterization of QCoh

Slogans by David Corwin

ll check: words starting with u, v, w, x, y, z, U, V, W, X, Y, or Z

LaTeX: \etale

Introduced the macro

\def\etale{{\acute{e}tale}}

and replaced all occurences of \acute{e}tale by \etale

move a chapter and rename a chapter

	We moved the chapter "Cohomology of Algebraic Spaces" earlier so
	we can use the results earlier in the treatment of algebraic
	spaces. Also, we finally renamed the chapter "Coherent
	Cohomology" to "Cohomology of Schemes" which is better.

Whitespace changes

Whitespace changes

LaTeX: Remove useless brackets

LaTeX: \Ob

	Introduced a macro

	\def\Ob{\mathop{\rm Ob}\nolimits}

	and replaced any occurence of \text{Ob}( with \Ob(. There are
	still some occurences of \text{Ob} but these are sets, not the
	operator that takes the set of objects of a category.

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

	and replaced all the occurences of \textit{Sch} with \Sch.

Adequate modules

	This material is a bit speculative. The idea is to find the
	smallest abelian subcategory of all sheaves of modules on a big
	site which contains the quasi-coherent ones. We succeed in doing
	this and characterizing these sheaves. However, there are some
	further issues with this category, one of them being that it
	isn't closed under tensor product...

Fixed references to short titles

	using the script we will add in the next commit

Fix references and labels

	Necessary because of addition of new chapter in previous commit.

Begin translating etale to \'etale or \acute{e}tale (in Math mode).

Spaces: Set theory: May always enlarge the base category of schemes

	modified:   descent.tex
	modified:   spaces.tex
	modified:   topologies.tex

Descent: Quasi-coherent sheaves in different topologies; done for now

	modified:   categories.tex
	modified:   descent.tex

TAGS: added new tags

	modified:   tags/tags

Descent: More on comparing quasi-coherent modules in various topologies

	TODO: Add proofs of the propositions stated in this commit

	modified:   descent.tex