Stable homotopy groups of spheres: from dimension 0 to 90

Abstract

Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic Adams spectral sequence for Ctau and the algebraic Novikov spectral sequence for BP_{*}, we compute the classical and motivic stable homotopy groups of spheres from dimension 0 to 90, except for some carefully enumerated uncertainties.