Volume 13, issue 1 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
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