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Localization for Thhku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories (Memoirs of the American Mathematical Society) - Softcover

Blumberg, Andrew J.; Mandell, Michael A.

 
9781470441784: Localization for Thhku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 1470441780 ISBN 13: 9781470441784
Publisher: Amer Mathematical Society, 2020

Synopsis

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 $A(*)$.

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  • PublisherAmer Mathematical Society
  • Publication date2020
  • ISBN 10 1470441780
  • ISBN 13 9781470441784
  • BindingPaperback
  • LanguageEnglish
  • Number of pages100

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