We study the tmf-based Adams spectral sequence for the type 2 spectrum Z. We
establish the structure of the E_1-page of this spectral sequence, and compute
the d_1-differential modulo v_2-torsion...We develop a technique for performing
low dimensional calculations, and use this to compute the spectral sequence
fully in stems < 40. We use this computation to prove that the K(2)-local
Adams-Novikov spectral sequence for Z studied by the third author and Egger
collapses, resulting in the computation of the homotopy groups of Z_{K(2)}. We
discuss how these computations fit with the conjectural failure of the
telescope conjecture.(read more)