The $v_1$-Periodic Region of the Complex-Motivic Ext

Abstract

We establish a $v_1$-periodicity theorem in Ext over the complex-motivic Steenrod algebra. The element $h_1$ of Ext, which detects the homotopy class $\eta$ in the motivic Adams spectral sequence, is non-nilpotent and therefore generates $h_1$-towers. Our result is that, apart from these $h_1$-towers, $v_1$-periodicity behaves as it does classically.