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

✍ Scribed by Andrew J. Blumberg; Michael A. Mandell

Publisher
American Mathematical Society
Year
2020
Tongue
English
Leaves
112
Series
Memoirs of the American Mathematical Society Ser.
Edition
1
Category
Library
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✦ 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 dΓ©vissage 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 $A(*)$.

✦ Subjects

K-theory. ; Algebraic topology. ; Cobordism theory. ; Homology theory.

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