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.

Another characterization of the use of "we" can be found in the introduction to  William Bloch's The Unimaginable Mathematics of Borges' Library of Babel:

This should not be construed as a “royal we.” It has been a construct of the community of mathematicians for centuries and it traditionally signifies two ideas: that “we” are all in consultation with each other through space and time, making use of each other’s insights and ideas to advance the ongoing human project of mathematics, and that “we”—the author and reader—are together following the sequences of logical ideas that lead to inexorable, and sometimes poetic, conclusions.

