Fortnightly links (76)

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–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.