Localization for $THH(ku)$ and the Topological Hochschild and Cyclic Homology of Waldhausen Categories 1

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Localization for $THH(ku)$ and the Topological Hochschild and Cyclic Homology of Waldhausen Categories

Andrew J Blumberg • Michael A Mandell

Pocket

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100 sidor
2021

The authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem. As applications, the authors prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding $THH(ku)$, and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on $A(*)$.

Författare: Andrew J Blumberg, Michael A Mandell
Format: Pocket/Paperback
ISBN: 9781470441784
Språk: Engelska
Antal sidor: 100
Utgivningsdatum: 2021-01-30
Förlag: American Mathematical Society