This talk is a report on joint work in progress with Lidia Angeleri-Hügel and Rosanna Laking. Our aim is to extend parts of the theory of large modules over tame hereditary algebras to arbitrary tame algebras. Let 𝐴 be a tame finite dimensional algebra over an algebraically closed field, and 𝜃 an additive functional on the Grothendieck group of 𝐴. Baumann, Kamnitzer and Tingley associate to 𝜃 a wide interval in the lattice of torsion classes of the category of finite dimensional 𝐴-modules, whose corresponding wide subcategory consists of the 𝜃-semistable 𝐴-modules in the sense of King. Angeleri-Hügel, Laking and Sentieri use cosilting theory to assign to such a wide interval a closed rigid subset of the Ziegler spectrum of the unbounded derived category of all 𝐴-modules. On the other hand, Plamondon associates to 𝜃 a generically 𝜏−-regular irreducible component of the scheme of 𝐴-modules. In this talk, we will explain how the closed rigid subset of the Ziegler spectrum is determined by generic modules constructed from the generically 𝜏−-regular irreducible com