Research Seminars @ Illinois

The stable homotopy groups of spheres are the most important and interesting invariants in stable homotopy theory. Computing these stable stems is a central task in the field. One approach to this task, inspired by chromatic homotopy theory, is to localize attention to periodic families in the stable stems. At the prime 2, Mahowald completely determined the v1-periodic stable stems by using the bo-resolution. In this talk, we will investigate an analogous question in motivic homotopy theory. In particular, there is a spectral sequence known as the kq-resolution which highlights v1-periodicity in the motivic stable stems. We will compute the E1-page of the kq-resolution over the real numbers and all finite fields.