This is a question of mathematical writing. Let me know if it would be better suited to academia.SE.

I am writing a paper in invariant theory. It uses some slightly heavy commutative algebra. There are a few points where I use facts of which I am convinced, and I believe they are widely known, but I am not sure how to look for a print reference. For example:

1) "flat of relative dimension $n$" is preserved under arbitrary base change

2) the functor of invariants commutes with flat base change

I learned (1) from Ravi Vakil's algebraic geometry notes (exercise 24.5.L). I learned (2) from the thesis of my coauthor (the proof is easy). There are other results like this I'm not thinking of right now that I probably learned from the Stacks Project.

I guess a thesis can be cited in print if needed, but it seems inappropriate to cite either Vakil's notes or the Stacks Project in a print article since they have not undergone formal peer-review, as authoritative as they are. I imagine I might be able to find one or both of these things in EGA, but then again, I might not, and I would spend a lot of time looking. As a young scholar, I do not yet feel I have a beat on what is regarded as common knowledge. My question is:

> What guidelines does one use to decide if results such as these require a reference in an article or can be used as common knowledge?