Using "we have" in maths papers I commonly want to use the phrase "we have" when writing mathematics, to mean something like "most readers will know this thing and I am about to use it". My primary question is whether this is too colloquial. My secondary question is what the alternatives are if it is too colloquial.
For example, right now I have a sentence
"Given a point $P\in X$ we have the residue map ${\text {res}}_P \colon \Omega_{K(X)} \rightarrow k$, as defined in ...". I don't feel saying "there exists the" is quite right. Even if it is grammatically correct, I don't think this conveys the implication that it will be almost certainly familiar to the expected audience.
I have seen this question but I feel this is slightly different. If not then my apologies.

interesting meta at "An impersonal and precise way of writing is important if we want to seem rigorous." [italics mine] 
Either the author is unaware or fiendishly clever!
I think "we have" and so on is already an established, rigorous math norm. 
Also, check out the Russian "imejem" which is the "have" of "we have", without "we". What is the Greek word? 
