Geometry & Topology 13 (2009) 319–357

DOI: 10.2140/gt.2009.13.319

Abstract

We characterize the 2–line of the p–local Adams–Novikov spectral sequence in terms of modular forms satisfying a certain explicit congruence condition for primes p ≥ 5. We give a similar characterization of the 1–line, reinterpreting some earlier work of A Baker and G Laures. These results are then used to deduce that, for ℓ a prime which generates Z_p^×, the spectrum Q(ℓ) detects the α and β families in the stable stems.

Keywords

topological modular forms, chromatic homotopy

Mathematical Subject Classification

Primary: 55Q45

Secondary: 11F33, 55N34, 55Q51

References

Publication

Received: 3 May 2008
Revised: 13 October 2008
Accepted: 8 October 2008
Preview posted: 5 November 2009
Published: 1 January 2009
Proposed: Paul Goerss
Seconded: Bill Dwyer, Haynes Miller

Authors