The stable Adams conjecture and higher associative structures on Moore spectra

• 成果类型: Article
• 署名作者: Bhattacharya, Prasit; Kitchloo, Nitu
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.195.2.1
• 发表日期: 2022
• 页码: 375-420
• 关键词: cohomology

摘要

In this paper, we provide a new proof of the stable Adams conjecture. Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the K-theory functor to a multinatural transformation. We also point out that the original proof of the stable Adams conjecture is incorrect and present a correction. This correction is crucial to our main application. We settle the question on the height of higher associative structures on the mod p(k) Moore spectrum M-p (k) at odd primes. More precisely, for any odd prime p, we show that M-p (k) admits a Thomified A(n)-structure if and only if n < p(k). We also prove a weaker result for p = 2.