Kyle M. Ormsby: Vanishing in motivic stable stems

Abstract: Recent work of Röndigs-Spitzweck-Østvær sharpens the connection between the slice and Novikov spectral sequences. Using classical vanishing lines for the E_2-page of the Adams-Novikov spectral sequence and the work of Andrews-Miller on the eta-periodic ANSS, I will deduce some new vanishing theorems in the bigraded homotopy groups of the eta-complete motivic sphere spectrum. In particular, I will show that the m-th eta-complete Milnor-Witt stem is bounded above (by an explicit piecewise linear function) when m = 1 or 2 (mod 4). This is joint work with Oliver Röndigs and Paul Arne Østvær.