Volume 13, issue 1 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Congruences between modular forms given by the divided $\beta$ family in homotopy theory

Mark Behrens

Geometry & Topology 13 (2009) 319–357
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 a prime which generates p×, the spectrum Q() detects the α and β families in the stable stems.

Keywords
topological modular forms, chromatic homotopy
Mathematical Subject Classification 2000
Primary: 55Q45
Secondary: 55Q51, 55N34, 11F33
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
Mark Behrens
MIT Department of Mathematics 2-273
77 Massachusetts Ave
Cambridge
MA 02140
USA
http://www-math.mit.edu/~mbehrens