• Amnon Neeman: Bounded t-structures on the category of perfect complexes proves that $\mathrm{Perf}X$ for a separated scheme $X$ (with some finiteness properties) has a bounded t-structure if and only if it is regular, in which case it actually has the obvious t-structure on $\mathrm{Perf}X=\mathbf{D}^{\mathrm{b}}(X)$. It also shows that on $\mathbf{D}^{\mathrm{b}}(X)$ all t-structures are in fact suitably equivalent. Cool!

• Qingyuan Jiang: Derived projectivizations of complexes describes the Proj of a complex of coherent sheaves (with amplitude in $[0,1]$), an object from derived algebraic geometry, and how their derived categories look like. This unifies many earlier results, and it's great to see this done in this level of sweeping generality.

• Alexander Kuznetsov: Derived categories of families of Fano threefolds is yet another beautiful paper by Sasha, on how the derived categories of Fano 3-folds behave when you consider them in families. I strongly recommend reading at least the introduction, as I won't be able to do it justice here.

He also managed to get one of the prettiest possible arXiv identifiers this month.