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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>τ</mml:mi> </mml:mrow> </mml:math> and the algebraic Novikov spectral sequence for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:msub> <mml:mi>P</mml:mi> <mml:mo>*</mml:mo> </mml:msub> </mml:mrow> </mml:math> , we compute the classical and motivic stable homotopy groups of spheres from dimension 0 to 90, except for some carefully enumerated uncertainties.