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

• 成果类型: Article
• 署名作者: Nave, Lee S.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.491
• 发表日期: 2010
• 页码: 491-509
• 关键词: division-algebras; spectral sequence; finite subgroups; stable homotopy; local-fields; spheres; MODULES

摘要

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.