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Coassembly and the $K$-theory of finite groups
- Source :
- Advances in Mathematics 307C (2017) pp. 100-146
- Publication Year :
- 2015
-
Abstract
- We study the $K$-theory and Swan theory of the group ring $R[G]$, when $G$ is a finite group and $R$ is any ring or ring spectrum. In this setting, the well-known assembly map for $K(R[G])$ has a companion called the coassembly map. We prove that their composite is the equivariant norm of $K(R)$. This gives a splitting of both assembly and coassembly after $K(n)$-localization, a new map between Whitehead torsion and Tate cohomology, and a partial computation of $K$-theory of representations in the category of spectra.<br />Comment: Accepted version. 44 pages
Details
- Database :
- arXiv
- Journal :
- Advances in Mathematics 307C (2017) pp. 100-146
- Publication Type :
- Report
- Accession number :
- edsarx.1503.06504
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.aim.2016.11.017