Prime thick subcategories on elliptic curves

Recently Matsui introduced the notion of prime thick subcategories in triangulated categories, and prove that the set of prime thick subcategories in a tensor triangulated category has a natural topology and contains the Balmer spectrum of the tensor triangulated category. In this talk, we discuss prime thick subcategories in derived categories of projective varieties. In particular, we determine the topological space of prime thick subcategories in derived categories of elliptic curves. This is a joint work with Genki Ouchi.