The Smith-Toda complex $V((p+1)/2)$ does not exist

Pages 491-509 from Volume 171 (2010), Issue 1 by Lee S. Nave

Abstract

Using a generalized homotopy fixed point spectral sequence due to Hopkins and Miller, we show that the Smith-Toda complex $V((p+1)/2)$ does not exist for $p$ a prime greater than 5. This extends earlier results of Toda and Ravenel for the primes 2, 3, and 5. It is also shown that if $V((p-1)/2)$ exists, it is not a ring spectrum.

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DOI
http://doi.org/10.4007/annals.2010.171.491
MR
2630045
Zbl
1194.55017
Milestones
Received: 16 November 2005
Accepted: 13 August 2008
Published online: 17 March 2010

Authors

Lee S. Nave