Here is the idea (stolen from the cring project): collect any expository notes written by you and put them on the web under the GFDL. Why? I have several reasons:

1. I have many times come across good expositions by younger people of (parts of) results in our field which ultimately disappear as the webpage is removed when the person moves on.
2. It turns out to be very helpful to use an initial write-up on some topic (no matter how badly written) to start a new chapter or a new section of the Stacks project.
3. Keep a record of past contributions in this form; this will allow people to compare the older version of material with what it transforms into in the Stacks project.
4. Expositions may cover results from the Stacks project sketching alternative proofs, more elementary treatments, etc.
5. Outlining more advanced material can be done in such notes, even if the necessary preliminaries aren’t yet available in the Stacks project.
6. Lower the threshold for participation in the Stacks project.

The last one because we’ll accept any latex source that compiles whose content is suitable (is about algebraic geometry, sheaves, commutative algebra, stacks, cohomology, dgas, etc).

I haven’t yet started a repository on github for this because I want your input on the name. It seems that using “incubator” is American English. Here are some (silly) alternative names for the repository: “Stacks dump”, “Stacks raw”, “Stacks stack” or “Stacks stock”. Please leave a comment if you have a preference for one of these or if you have another (sillier) name to suggest.

Once the repository goes up we can after a while set up a web page which displays compiled (pdf) versions of these notes somewhere. We can have a big sign telling the casual visitor that these notes are just there in the hope that they will help out understanding the material.

I will try to initially populate the repository with latex files sent to me over the past 6 years some of which have already gone into the Stacks project and some of which haven’t. (If this concerns you I will email you and ask for your permission before I do so, or you can email me to remind me.) Also, please feel free to email me anything that fits the description given above (stacks.project@gmail.com).

Note, note, note: You can do whatever you want with material you write yourself; you own it. To emphasize this, I always suggest people who contribute material to the Stacks project, to keep a copy of their work on their webpage, or post it on the arxiv, or whatever. The same is true for submitting to the incubator (or whatever it will be called). If later you realize you want to turn whatever you contributed into a paper (to be published) you can certainly do so (and at your request we can even remove anything you contributed, as long as it hasn’t gone into the Stacks project yet).

Finally, if you have a friend with a nice write-up, gently suggest they consider the incubator…