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I have a preprint on the arXiv, a couple of years old, and will shortly be re-submitting an updated version. The changes are fairly limited — more than just typos, but not so much as to change the section numbering, let’s say.

I and a co-author are postdocs, and have moved institutions since the original version. Should we update the author affiliations as given in the article, or leave them as they are?

The article hasn’t been published and probably won’t be any time soon (it’s expository, and a bit difficult to find a suitable venue for). However, it’s been fairly widely read and cited as a preprint.

The field is pure mathematics.

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    I'm not sure of the norms here so won't put an answer in, but worth remembering that if you don't feel right updating the affiliations, you could consider adding a footnote - "(*) now at University of X, [email protected]" or similar
    – Andrew is gone
    Commented Mar 2, 2016 at 10:49
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    If you're using LaTeX, check whether the style file that you use allows for a "current address" in addition to the main affiliation.
    – Andreas Blass
    Commented Mar 3, 2016 at 0:22

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Your affiliation as far as the work goes is where the work was done. You should perhaps add a footnote giving your current location, and (obviously) update any contact information given.

Or do it the the other way around: give current affiliation, and in acknowledgements or at least a footnote state where the work was done.

I've seen both.

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