Glen Matthew Wilson: The eta-inverted sphere over the rationals

Abstract: Guillou and Isaksen, with input from Andrews and Miller, have calculated the motivic stable homotopy groups of the two-complete sphere spectrum after inverting multiplication by the Hopf map eta over the fields R and C. We will review these known results and show how to calculate the motivic stable homotopy groups of the two-complete eta-inverted sphere spectrum over fields of cohomological dimension at most two with characteristic different from 2 and the field of rational numbers.