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| Softcover ISBN: | 978-1-4704-4178-4 |
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| Softcover ISBN: | 978-1-4704-4178-4 |
| Product Code: | MEMO/265/1286 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-6140-9 |
| Product Code: | MEMO/265/1286.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-4178-4 |
| eBook ISBN: | 978-1-4704-6140-9 |
| Product Code: | MEMO/265/1286.B |
| List Price: | $170.00 $127.50 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 265; 2020; 100 ppMSC: Primary 19; Secondary 55
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 dévissage 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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Table of Contents
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Chapters
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Introduction
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1. Review of $THH$, $TR$, and $TC$
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2. $THH$ and $TC$ of simplicially enriched Waldhausen categories
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3. $K$-theory theorems in $THH$ and $TC$
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4. Localization sequences for $THH$ and $TC$
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5. Generalization to Waldhausen categories with factorization
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Additional Material
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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 dévissage 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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Chapters
-
Introduction
-
1. Review of $THH$, $TR$, and $TC$
-
2. $THH$ and $TC$ of simplicially enriched Waldhausen categories
-
3. $K$-theory theorems in $THH$ and $TC$
-
4. Localization sequences for $THH$ and $TC$
-
5. Generalization to Waldhausen categories with factorization
