I agree with RvDdB's answer, but want to add some thoughts. To quote from another SE answer of mine:

First, my general philosophy is that one should try to make papers reasonably accessible to young people who have not spent months or years working on this specific problem. I generally feel that most math papers should do a better job of providing references than they do.

There I also espouse the view that writing (and reading) papers and getting feedback (via reviews, discussions, questions during/after talks) provides a process whereby you learn what is more common knowledge to other people in your field and what is less common. When you are young (and sometimes even when you're not), you probably don't have a good sense of this, so it's good to err on the safe side of including a citation if you're not sure, and often a referee will help you out by suggesting a citation is needed (or less often, not needed).

But one rule of thumb is: think about what you knew before you started working on this specific problem. You may need to modify this depending on your situation (e.g., if you started working on the problem before you knew anything about the field), but perhaps thinking about this sentiment is still helpful.

Anyway, the main thing I wanted to add to the already existing answers is: think about your intended audience. I would give this advice for writing the paper in general, and it's also applicable to your particular question. For instance, if I'm writing a paper targeted at people who do local representation theory I might not bother to reference some basic properties of the local Jacquet-Langlands correspondence known 30-40 years ago (e.g., the correspondence for 1-dimensionals of division algebras), but if I think my paper should be of interest to, say, people in classical modular forms who aren't all experts in local representation theory, then I definitely will. (I'm not saying that the amount of time passed since a result was known should be the only factor here--the older less well known facts I would also cite.)

Do you think your paper will/should be of interest to people who aren't intimately familiar with properties of base change? If so, try to provide a citation.