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CONGRUENCES BETWEEN MODULAR FORMS GIVEN BY THE DIVIDED β FAMILY IN HOMOTOPY THEORY

By Mark Behrens

Abstract

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 a computation of A. Baker. 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. Content

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.817
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