Moonshine over the integers

I’d been meaning to write a plug for my paper A self-dual integral form for the moonshine module on this blog for almost 7 years, but never got around to it until now. It turns out that sometimes, if you wait long enough, someone else will do your work for you. In this case, I recently noticed that Lieven Le Bruyn wrote up a nice summary of the result in 2021. I thought I’d add a little history of my own interaction with the problem. I first ran into this question when reading Borcherds and...