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The Strong Künneth Theorem for Topological Periodic Cyclic Homology
 
Andrew J. Blumberg Columbia University, New York, New York
Michael A. Mandell Indiana University, Bloomington, Indiana
Softcover ISBN:  978-1-4704-7138-5
Product Code:  MEMO/301/1508
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-7952-7
Product Code:  MEMO/301/1508.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7138-5
eBook: ISBN:  978-1-4704-7952-7
Product Code:  MEMO/301/1508.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
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The Strong Künneth Theorem for Topological Periodic Cyclic Homology
Andrew J. Blumberg Columbia University, New York, New York
Michael A. Mandell Indiana University, Bloomington, Indiana
Softcover ISBN:  978-1-4704-7138-5
Product Code:  MEMO/301/1508
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-7952-7
Product Code:  MEMO/301/1508.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7138-5
eBook ISBN:  978-1-4704-7952-7
Product Code:  MEMO/301/1508.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 3012024; 102 pp
    MSC: Primary 19

    View the abstract.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Orthogonal $G$-spectra and the Tate fixed points
    • 3. A lax Künneth theorem for Tate fixed points
    • 4. The Tate spectral sequences
    • 5. Topological periodic cyclic homology
    • 6. A filtration argument (Proof of Theorem A)
    • 7. Filtered modules over filtered ring orthogonal spectra
    • 8. Comparison of the lefthand and righthand spectral sequences (Proof of Theorem 6.3)
    • 9. Conditional convergence of the lefthand spectral sequence (Proof of Lemma 6.5)
    • 10. Constructing the filtered model: The positive filtration
    • 11. Constructing the filtered model: The negative filtration
    • 12. Constructing the filtered model and verifying the hypotheses of Chapter 6
    • 13. The $E^1$-term of the Hesselholt-Madsen $\mathbb {T}$-Tate spectral sequence
    • 14. Comparison of the Hesselholt-Madsen and Greenlees $\mathbb {T}$-Tate Spectral Sequences
    • 15. Coherence of the equivalences $E\mathbb {T}/E\mathbb {T}_{2n-1}\simeq E\mathbb {T}_{+}\wedge S^{\mathbb {C}(1)^{n}}$ (Proof of Lemma 13.3)
    • 16. The strong Künneth theorem for $THH$
    • 17. $THH$ of smooth and proper algebras (Proof of Theorem C)
    • 18. The finiteness theorem for $TP$ (Proof of Theorem B)
    • 19. Comparing monoidal models
    • 20. Identification of the enveloping algebras and $\operatorname {Bal}$
    • 21. A topologically enriched lax symmetric monoidal fibrant replacement functor for equivariant orthogonal spectra (Proof of Lemma 3.1)
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 3012024; 102 pp
MSC: Primary 19

View the abstract.

  • Chapters
  • 1. Introduction
  • 2. Orthogonal $G$-spectra and the Tate fixed points
  • 3. A lax Künneth theorem for Tate fixed points
  • 4. The Tate spectral sequences
  • 5. Topological periodic cyclic homology
  • 6. A filtration argument (Proof of Theorem A)
  • 7. Filtered modules over filtered ring orthogonal spectra
  • 8. Comparison of the lefthand and righthand spectral sequences (Proof of Theorem 6.3)
  • 9. Conditional convergence of the lefthand spectral sequence (Proof of Lemma 6.5)
  • 10. Constructing the filtered model: The positive filtration
  • 11. Constructing the filtered model: The negative filtration
  • 12. Constructing the filtered model and verifying the hypotheses of Chapter 6
  • 13. The $E^1$-term of the Hesselholt-Madsen $\mathbb {T}$-Tate spectral sequence
  • 14. Comparison of the Hesselholt-Madsen and Greenlees $\mathbb {T}$-Tate Spectral Sequences
  • 15. Coherence of the equivalences $E\mathbb {T}/E\mathbb {T}_{2n-1}\simeq E\mathbb {T}_{+}\wedge S^{\mathbb {C}(1)^{n}}$ (Proof of Lemma 13.3)
  • 16. The strong Künneth theorem for $THH$
  • 17. $THH$ of smooth and proper algebras (Proof of Theorem C)
  • 18. The finiteness theorem for $TP$ (Proof of Theorem B)
  • 19. Comparing monoidal models
  • 20. Identification of the enveloping algebras and $\operatorname {Bal}$
  • 21. A topologically enriched lax symmetric monoidal fibrant replacement functor for equivariant orthogonal spectra (Proof of Lemma 3.1)
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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