• Benjamin Antieau is now blogging. Check out his blog for lucid writeups of new developments in K-theory, Hochschild homology, de Rham cohomology and related topics! I personally greatly enjoy this initiative, as I'm reasonably close to the subject, but far from an insider, so thank you Ben for discussing interesting examples that help me to grok what's going on in the area!

  • q.uiver.app is an online editor for complicated TikZ diagrams. It seems to be the best I have seen so far, and I might even try it myself for some of the more exotic things I need to produce. See also the announcing blogpost/.

  • Dmitrii Pirozhkov: Stably semiorthogonally indecomposable varieties introduces a stronger version of the notion of indecomposable derived category. What is so interesting about it is that it implies indecomposability (but is quite a bit stronger, e.g. not all K3 surfaces are not stably indecomposable, because closed subvarieties of stable indecomposables are again stably indecomposable, but some K3 surfaces contain a $\mathbb{P}^1$, which is decomposable), and that there is a sufficient criterion for it (namely mapping finitely to the Albanese variety).

    Does anyone know which class of surfaces of general type has this property? Or which smooth projective surfaces of general type contain a smooth rational curve? Some Horikawa surfaces have this, which tells us they are not stably indecomposable, even though all of them have an indecomposable derived category. So I guess this is a Kodaira dimension 2 version of Example 2.4.