The first Adams-Novikov differential for the spectrum T (m), Available on the author’s website

Abstract. There are p-local spectra T (m) with BP∗(T (m)) = BP∗[t1,..., tm]. In this paper we determine the first nontrivial differential in the Adams– Novikov spectral sequence for each of them for p odd. For m = 0 (the sphere spectrum) this is the Toda differential, whose source has filtration 2 and whose target is the first nontrivial element in filtration 2p + 1. The same goes for m = 1, and for m> 1 the target is v2 times the first such element. The proof uses the Thomified Eilenberg-Moore spectral sequence. We also estab-lish a vanishing line and the behavior near it in the Adams–Novikov spectral sequence for T (m). This paper concerns the Adams–Novikov spectral sequence for the spectra T (m) introduced in [Rav86, §6.5]. We begin by recalling their basic properties. For each prime p and natural number m there is a p-local spectrum T (m) such that BP∗(T (m)) = BP∗[t1,..., tm] ⊂ BP∗(BP) as a comodule algebra over BP∗(BP). It is a summand of the p-localization of the Thom spectrum of the stable bundle induced b