Viktor Balch Barth (UiO) - Making the motivic group structure on the endomorphisms of the projective line explicit

In this talk, I explain how we explicitly construct a motivic analog of the fundamental group of the circle. We construct a group structure on the set of pointed naive homotopy classes of maps from the Jouanolou device to the projective line. The group operation is defined via matrix multiplication on generating sections of line bundles and only requires basic algebraic geometry. In particular, it is completely independent of the construction of the motivic homotopy category. Based on joint work with William Hornslien, Gereon Quick, and Glen Matthew Wilson.