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The Resource Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories, (electronic resource)

Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories, (electronic resource)

Label
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
Creator
Contributor
Language
eng
Summary
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(*)
Member of
Cataloging source
NhCcYBP
http://library.link/vocab/creatorName
Blumberg, Andrew J
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Mandell, Michael A
  • ProQuest (Firm)
Series statement
Memoirs of the American Mathematical Society Ser.
Series volume
v.265
Label
Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover -- Title page -- Introduction -- Chapter 1. Review of , , and -- 1.1. Review of spectral categories -- 1.2. Review of the construction of , , and -- 1.3. Review of the invariance properties of -- 1.4. The Dennis-Waldhausen Morita Argument -- Chapter 2. and of simplicially enriched Waldhausen categories -- 2.1. Simplicially enriched Waldhausen categories -- 2.2. Spectral categories associated to simplicially enriched Waldhausen categories -- 2.3. The \Sdot and Moore nerve constructions -- 2.4. The Moore \Spdot construction
  • 2.5. , , and the cyclotomic trace -- Chapter 3. -theory theorems in and -- 3.1. The Additivity Theorem -- 3.2. The Cofiber Theorem -- 3.3. The Localization Theorem -- 3.4. The Sphere Theorem -- 3.5. Proof of the Sphere Theorem -- Chapter 4. Localization sequences for and -- 4.1. The localization sequence for of a discrete valuation ring -- 4.2. The localization sequence for ( ) and related ring spectra -- 4.3. Proof of the Dévissage Theorem -- Chapter 5. Generalization to Waldhausen categories with factorization -- 5.1. Weakly exact functors
  • 5.2. Embedding in simplicially tensored Waldhausen categories -- 5.3. Spectral categories and Waldhausen categories -- Bibliography -- Index -- Back Cover
Control code
MSTDDA6229929
Dimensions
unknown
Extent
1 online resource ( 112 p..):
Form of item
online
Isbn
9781470461409
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reproduction note
Electronic reproduction.
Specific material designation
remote
Label
Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories, (electronic resource)
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover -- Title page -- Introduction -- Chapter 1. Review of , , and -- 1.1. Review of spectral categories -- 1.2. Review of the construction of , , and -- 1.3. Review of the invariance properties of -- 1.4. The Dennis-Waldhausen Morita Argument -- Chapter 2. and of simplicially enriched Waldhausen categories -- 2.1. Simplicially enriched Waldhausen categories -- 2.2. Spectral categories associated to simplicially enriched Waldhausen categories -- 2.3. The \Sdot and Moore nerve constructions -- 2.4. The Moore \Spdot construction
  • 2.5. , , and the cyclotomic trace -- Chapter 3. -theory theorems in and -- 3.1. The Additivity Theorem -- 3.2. The Cofiber Theorem -- 3.3. The Localization Theorem -- 3.4. The Sphere Theorem -- 3.5. Proof of the Sphere Theorem -- Chapter 4. Localization sequences for and -- 4.1. The localization sequence for of a discrete valuation ring -- 4.2. The localization sequence for ( ) and related ring spectra -- 4.3. Proof of the Dévissage Theorem -- Chapter 5. Generalization to Waldhausen categories with factorization -- 5.1. Weakly exact functors
  • 5.2. Embedding in simplicially tensored Waldhausen categories -- 5.3. Spectral categories and Waldhausen categories -- Bibliography -- Index -- Back Cover
Control code
MSTDDA6229929
Dimensions
unknown
Extent
1 online resource ( 112 p..):
Form of item
online
Isbn
9781470461409
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reproduction note
Electronic reproduction.
Specific material designation
remote

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