Tuesday, May 3, 14:00
Martin Kalck (Freiburg), Update on singularity categories.
We will start with an introduction to singularity categories, which were
by Buchweitz and later rediscovered by Orlov.
Then we will explain what is known about triangle equivalences between
singularity categories of commutative rings, recalling
results of Knörrer, D. Yang (based on our joint works on relative
singularity categories. This also follows from work of Kawamata and was
generalized in a joint work with Karmazyn) and a new equivalence obtained in
We will then focus on the case of Gorenstein isolated singularities and
especially hypersurfaces, where we give a
complete description of quasi-equivalence classes of dg enhancements of
singularity categories, answering a question of Keller & Shinder.
This is based on arXiv:2108.03292.