Fabio Tanania (TU Darmstadt)

In this talk, I will introduce the isotropic stable motivic homotopy category, which is a stable homotopic version of Vishik’s category of isotropic motives. These are local versions of the classical motivic categories SH(k) and DM(k), obtained roughly speaking by annihilating motives of anisotropic varieties. When the base field k is flexible, then isotropic motivic categories have a lot of remarkable properties. As an example, I will describe the structure of cellular isotropic spectra in terms of well-known objects coming from classical homotopy theory. Then, I will discuss what is known about the non-cellular part of isotropic motivic categories and state some open questions.