On the E2‐term of the bo‐Adams spectral sequence. Issue 1 (11th January 2020) - Beaudry, A.; Behrens, M.; Bhattacharya, P.; Culver, D.; Xu, Z.
Abstract: The E 1 ‐term of the (2‐local) bo ‐based Adams spectral sequence for the sphere spectrum decomposes into a direct sum of a v 1 ‐periodic part, and a v 1 ‐torsion part. Lellmann and Mahowald completely computed the d 1 ‐differential on the v 1 ‐periodic part, and the corresponding contribution to the E 2 ‐term. The v 1 ‐torsion part is harder to handle, but with the aid of a computer it was computed through the 20‐stem by Davis. Such computer computations are limited by the exponential growth of v 1 ‐torsion in the E 1 ‐term. In this paper, we introduce a new method for computing the contribution of the v 1 ‐torsion part to the E 2 ‐term, whose input is the cohomology of the Steenrod algebra. We demonstrate the efficacy of our technique by computing the bo ‐Adams spectral sequence beyond the 40‐stem.