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

Blumberg, Andrew J./ Mandell, Michael A.

American Mathematical Society（2021/01発売）

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製本 Paperback:紙装版/ペーパーバック版／ページ数 100 p.
言語 ENG
商品コード 9781470441784
DDC分類 514

Full Description

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 $A(*)$.