Cosupport in tensor-triangulated geometry

We will give an introduction to the theory of cosupport in tensor-triangulated geometry, dual to the Balmer–Favi notion of support. This gives a method of classifying the colocalizing coideals of a tensor-triangulated category in terms of subsets of its spectrum of prime ideals. We will explain how this recovers and unifies a number of classification theorems in the literature, and give some new examples. This is joint work with Tobias Barthel, Natalia Castellana, and Beren Sanders