# Fortnightly links (70)

Guest post by Kevin Buzzard is an excellent explanation of the kind of issues one runs into when trying to formalise some basic results regarding sheaf theory, as part of Kevin Buzzard's experiment to formalise parts of the Stacks project. I occasionaly get asked questions about formalising the Stacks project, about which I can say absolutely nothing, but now I can start referring to this post.

Kenta Ueyama, On Knörrer periodicity for quadric hypersurfaces in skew projective spaces is a fun paper describing the singularity categories of quadric hypersurfaces

*in skew polynomial rings*, where necessarily all structure coefficients are $\pm 1$. The interesting feature is that the size of the category grows (measured by number of factors equivalent to $\mathbf{D}^{\mathrm{b}}(k)$) the more noncommutative (measured by the size of the point scheme) one gets. It'd be interesting to figure out the general pattern, and find a good geometric description for this behavior!OWR Report for the Arbeitsgemeinschaft: Topological cyclic homology is the report for a week-long Arbeitsgemeinschaft which happened earlier this year at Oberwolfach.