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I am almost ready to submit my most recent paper, and I find myself in a problem that has already occurred multiple times in my short publishing career. In this paper, I wish to state a result which I consider 'well-known', but a skimming of all the likely textbooks and survey articles doesn't yield a nice statement that I can cite. For reference, the result in question is the following:

Let $X$ be a smooth, affine variety over $\mathbb{C}$, with coordinate ring $\mathcal{O}_X$. Then there is a natural isomorphism of $\mathcal{O}_X$-modules from the Kahler differentials $\Omega(\mathcal{O}_X)$ of $\mathcal{O}_X$ to the global 1-forms on $X$ with regular coefficients.

This is a result whose proof I know, and is homework-level difficulty, but including the proof in my short paper would require terminology and techniques I'd rather not introduce and consume precious space. It's also not a necessary result for the paper; I am including it to justify the study of Kahler differentials to an audience which might include differential geometers.

So what does one do in this situation? The lazy solution is to include some weasel words to avoid finding a citation ("it is a straight-forward exercise to show that..."), but this seems like a dangerous policy to employ in general. However, finding a citation is proving unreasonably time-consuming, since its it's not in the books I know (Hartshorne, Eisenbud, Kunz), and each new book/article I skim has its own notation and assumptions.

Also, while I'd be extremely grateful for a citation for the specific result above, my question is about what to do in this kind of situation. I'm trying not to get the answers mixed up.

I am almost ready to submit my most recent paper, and I find myself in a problem that has already occurred multiple times in my short publishing career. In this paper, I wish to state a result which I consider 'well-known', but a skimming of all the likely textbooks and survey articles doesn't yield a nice statement that I can cite. For reference, the result in question is the following:

Let $X$ be a smooth, affine variety over $\mathbb{C}$, with coordinate ring $\mathcal{O}_X$. Then there is a natural isomorphism of $\mathcal{O}_X$-modules from the Kahler differentials $\Omega(\mathcal{O}_X)$ of $\mathcal{O}_X$ to the global 1-forms on $X$ with regular coefficients.

This is a result whose proof I know, and is homework-level difficulty, but including the proof in my short paper would require terminology and techniques I'd rather not introduce and consume precious space. Its It's also not a necessary result for the paper; I am including it to justify the study of Kahler differentials to an audience which might include differential geometers.

So what does one do in this situation? The lazy solution is to include some weasel words to avoid finding a citation ("it is a straight-forward exercise to show that..."), but this seems like a dangerous policy to employ in general. However, finding a citation is proving unreasonably time-consuming, since its not in the books I know (Hartshorne, Eisenbud, Kunz), and each new book/article I skim has its own notation and assumptions.

Also, while I'd be extremely grateful for a citation for the specific result above, my question is about what to do in this kind of situation. I'm trying not to get the answers mixed up.

Let $X$ be a smooth, affine variety over $\mathbb{C}$, with coordinate ring $\mathcal{O}_X$. Then there is a natural isomorphism of $\mathcal{O}_X$-modules from the Kahler differentials $\Omega(\mathcal{O}_X)$ of $\mathcal{O}_X$ to the global 1-forms on $X$ with regular coefficients.