# Fortnightly links (52)

Daniel Bergh and Olaf Schnürer, Conservative descent for semi-orthogonal decompositions is a preprint that explains rigorously how one can study semi-orthogonal decompositions locally on an algebraic stack. It is interesting to see the generality in which this holds, and to see this applied to the examples in the literature (blowups, projective bundles and root stacks) in a greater generality.

Grzegorz Kapustka, Michał Kapustka and Riccardo Moschetti, Equivalence of K3 surfaces from Verra threefolds is a preprint that gives examples of degree 2 K3 surfaces which are non-isomorphic, but which are derived equivalent and their difference in the Grothendieck ring of varieties is annihilated by a power of the affine line. It's always nice to see some Macaulay2 code appearing, showing how such questions can also have a computer algebra component in them.

Yuri Prokhorov, The rationality problem for conic bundles is an expository preprint on (you never guess), the rationality problem for (3-dimensional) conic bundles. This is a particularly subtle problem, with links to noncommutative algebraic geometry.