Abstract: I will discuss the tensor-triangulated geometry of the stable motivic homotopy category SH(k) and a big family of the so-called isotropic realisation functors, parameterized by the choices of a Morava K-theory and an extension of the base field k (of characteristic zero). By studying the target category of such an isotropic realisation functor, we are able to construct the so-called isotropic Morava points of the Balmer spectrum Spc(SH(k)^c) of the stable motivic homotopy category SH(k). This is based on joint work with Alexander Vishik.
