Jarod Alper, Daniel Halpern-Leistner, Jochen Heinloth: Existence of moduli spaces for algebraic stacks is a long-anticipated preprint (at least, we've been running a seminar about it in Bonn). Recall that the Keel&ndas;Mori theorem says that an algebraic stack with finite inertia (i.e. the map from the inertia stack to the stack is finite) admits a coarse moduli space. Without one needs the notion of a good moduli space, which works significantly more generally but one loses the bijection on geometric points.
Benjamin Antieau: On the uniqueness of infinity-categorical enhancements of triangulated categories is a very interesting preprint, not only because it discusses enhancements of triangulated categories in the $\infty$-categorical setting using novel methods and a systematic application of t-structures. It ends with almost 15 pages of suggestions, speculations, and examples. For instance, it is explained why the methods cannot be applied to singularity categories (where non-uniqueness of enhancements is known to hold).
Yuri Prokhorov: Classification of smooth Fano 3-folds are videos of a 10-talk lecture series on the classification of Fano 3-folds, at the Institue for Basic Science in South Korea.