The Stacks Project Algebraic Stacks And The Algebraic Geometry Needed To Define Them The Stacks Project by The Stacks Project instant download after payment.

This is the home page of the Stacks project. It is an open source textbook and reference work on algebraic stacks and the algebraic geometry needed to define them.
The Stacks project started in 2005. The initial idea was for it to be a collaborative web-based project with the aim of writing an introductory text about algebraic stacks. Temporarily there was a mailing list and some discussion as to how to proceed. For example, there are issues with referencing such a document, how to distribute credit, who does what, and many more. Although we have definite ideas about most of these points we would like to take a more positive approach. Namely, to simply create something and solve problems and answer questions as they come up.
We do want to answer a few basic questions that the casual visitor may have about this project:
The Stacks project is no longer an introductory text, but aims to build up enough basic algebraic geometry as foundations for algebraic stacks. This implies a good deal of theory on commutative algebra, schemes, varieties, algebraic spaces, has to be developed en route.
The Stacks project has a maintainer (currently Aise Johan de Jong) who accepts changes etc. proposed by contributors. Although everyone is encouraged to participate it is not a wiki.
The Stacks project is meant to be read online, and therefore we do not worry about length of the chapters, etc. Moreover, with hyperlinks it is possible to quickly browse through the chapters to find the lemmas, theorems, etc. that a given result depends on.
http://stacks.math.columbia.edu/
https://github.com/stacks/stacks-project