Fortnightly links (156)
Pablo Magni: Derived equivalences of generalized Kummer varieties discusses when the generalised Kummer variety of an abelian variety and the dual abelian variety are derived equivalent. The cool thing about these results is that these generalised Kummers are in general not birational, thus their derived equivalence is not predicted by the Bondal–Orlov conjecture.
It is also explained (near the end of the introduction) how it might not be the case that $A$ and $A^\vee$ always give rise to derived equivalent generalised Kummers. Cool!
Amnon Neeman: Obstructions to the existence of bounded t-structures is a wonderful survey discussing when categories can be shown not to admit bounded t-structures. Given the crucial role that t-structures have in algebra and geometry, it is interesting to find obstructions and prove they are non-zero in relevant cases. As often with Amnon's writing, this is a highly recommended read. For instance the buildup to Theorem 5.8 is great to read. I wish more researchers would write surveys like this one!
categorical-examples is a newly developed tool to comb through combinations of properties of rings, modules, schemes, sheaves, and morphisms between these. It is built on top of Lean, so using it benefits from having seen this before. In any case it is a great tool for accessing a large library of results and finding examples.
Also, I was told that Lean has produced some of these examples using an automatic search, rather than someone explicitly describing them. I'd love to see more about this!