Coassembly and the K-theory of finite groups

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• 作者：Cary Malkiewich ^{cmalkiew@illinois.edu}
• 关键词：Algebraic K-theory ; Assembly ; Transfer map ; Parametrized spectrum
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：307
• 期：Complete
• 页码：100-146
• 全文大小：677 K
• 卷排序：307

文摘

We study the K  -theory and Swan theory of the group ring R[G]R[G], when G is a finite group and R   is any ring or ring spectrum. In this setting, the well-known assembly map for K(R[G])K(R[G]) has a companion called the coassembly map. We prove that their composite is the equivariant norm of K(R)K(R). This gives a splitting of both assembly and coassembly after K(n)K(n)-localization, a new map between Whitehead torsion and Tate cohomology, and a partial computation of K-theory of representations in the category of spectra.