Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories

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 prov...

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Detalles Bibliográficos
Autores principales: Blumberg, Andrew J, Mandell, Michael A
Lenguaje:eng
Publicado: American Mathematical Society 2020
Materias:
XX
Acceso en línea:http://cds.cern.ch/record/2744815
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author Blumberg, Andrew J
Mandell, Michael A
author_facet Blumberg, Andrew J
Mandell, Michael A
author_sort Blumberg, Andrew J
collection CERN
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 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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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2020
publisher American Mathematical Society
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spelling cern-27448152021-04-21T16:44:53Zhttp://cds.cern.ch/record/2744815engBlumberg, Andrew JMandell, Michael ALocalization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categoriesXXThe 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(*).American Mathematical Societyoai:cds.cern.ch:27448152020
spellingShingle XX
Blumberg, Andrew J
Mandell, Michael A
Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories
title Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories
title_full Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories
title_fullStr Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories
title_full_unstemmed Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories
title_short Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories
title_sort localization for $thh(ku)$ and the topological hochschild and cyclic homology of waldhausen categories
topic XX
url http://cds.cern.ch/record/2744815
work_keys_str_mv AT blumbergandrewj localizationforthhkuandthetopologicalhochschildandcyclichomologyofwaldhausencategories
AT mandellmichaela localizationforthhkuandthetopologicalhochschildandcyclichomologyofwaldhausencategories

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