Xander Faber, Jon Grantham, Everett W. Howe: On the Maximum Gonality of a Curve over a Finite Field is one of these preprints that makes me as an outsider smile at the beauty of the mathematics that I don't work on.
They also mention an example of a pair of curves of genus 3 with non-polarised isomorphic Jacobians, but one of them being a plane quartic and the other a hyperelliptic curve. Fun!
Jürgen Werner, Simon Venter, Nicolas Addington: Small resolutions of special three-dimensional varieties is the English translation of the first author's PhD thesis on explicit resolutions of 3-folds. This is a beautiful subject, and Werner's work made an appearance in what Thorsten and I did on homological projective duality for the Segre cubic.
Jon Sterling: Problèmes dans les topos is not something I link for its contents, but rather for the infrastructure used. There exists a system that allows you to write mathematics and use a tag-based referencing system (like the Stacks project does) without the hassle of using Gerby. Another instance is Jon's Foundations of relative category theory. They're based on krater. The setup is very different from how one would use Gerby though, but it has the benefit of being something completely static and low-maintenance.