K-theoretic Tate-Poitou duality and the fiber of the cyclotomic trace
成果类型：
Article
署名作者：
Blumberg, Andrew J.; Mandell, Michael A.
署名单位：
University of Texas System; University of Texas Austin; Indiana University System; Indiana University Bloomington
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-020-00952-z
发表日期：
2020
页码：
397-419
关键词：
摘要：
Let p is an element of Zbe an odd prime. We prove a spectral version of Tate-Poitou duality for the algebraic K-theory spectra of number rings with p inverted. This identifies the homotopy type of the fiber of the cyclotomic trace K(OF)p perpendicular to -> TC(OF)p perpendicular to TC after taking a suitably connective cover. As an application, we identify the homotopy type at odd primes of the homotopy fiber of the cyclotomic trace for the sphere spectrum in terms of the algebraic K-theory of Z.
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