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

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

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
Subject
Genre
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
EBLCP
http://library.link/vocab/creatorName
Blumberg, Andrew J
Dewey number
512/.66
Index
index present
LC call number
QA612.33
LC item number
.B56 2020eb
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Mandell, Michael A
Series statement
Memoirs of the American Mathematical Society Ser.
Series volume
no. 1286
http://library.link/vocab/subjectName
  • K-theory
  • Algebraic topology
  • Cobordism theory
  • Homology theory
  • Algebraic topology
  • Cobordism theory
  • Homology theory
  • K-theory
  • $K$-theory [See also 16E20, 18F25] -- Higher algebraic $K$-theory -- $K$-theory and homology; cyclic homology and cohomology [See also 18G60]
  • Algebraic topology -- Homotopy theory {For simple homotopy type, see 57Q10} -- Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
  • $K$-theory [See also 16E20, 18F25] -- Topological $K$-theory [See also 55N15, 55R50, 55S25] -- Connective $K$-theory, cobordism [See also 55N22]
  • $K$-theory [See also 16E20, 18F25] -- Higher algebraic $K$-theory -- Algebraic $K$-theory of spaces
Label
Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories
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
1159163192
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
Specific material designation
remote
System control number
(OCoLC)1159163192
Label
Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories
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
1159163192
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
Specific material designation
remote
System control number
(OCoLC)1159163192

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