# Fortnightly links (69)

Because of my holiday the schedule has been shifted by a week, and the post is 2 days late.

The spectrum of the integers is not quasi-compact is the title of a newly added example in the Stacks project. It sounds of course ridiculous to claim that $\mathop{\mathrm{Spec}}\mathbb{Z}$ is not quasicompact. But this is for the canonical topology on the category of schemes, which is of course much finer than the Zariski topology!

Srikanth Iyengar, Ryo Takahashi, Openness of the regular locus and generators for module categories is a nice and short paper which relates the regularity properties of (quotients of) a noetherian ring $R$ to the existence of (classical) generators in the bounded derived category (resp. singularity category) of $R$. This can be compared to Neeman's results on the existence of

*strong*generators, as is also done in remark 2.12 of their paper.Janko Boehm, Wolfram Decker, Anne Frühbis-Krüger, Franz-Josef Pfreundt, Mirko Rahn, Lukas Ristau, Towards massively parallel computations in algebraic geometry discusses one of the first steps in parallelizing computations in algebraic geometry. This is a really exciting evolution. If the authors read this, they could take up Borisov and Keum's Explicit equations of a fake projective plane as another example of a surface of general type with explicit but very complicated equations.