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The Strong Künneth Theorem for Topological Periodic Cyclic Homology
Softcover ISBN:  9781470471385 
Product Code:  MEMO/301/1508 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470479527 
Product Code:  MEMO/301/1508.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471385 
eBook: ISBN:  9781470479527 
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
Softcover ISBN:  9781470471385 
Product Code:  MEMO/301/1508 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470479527 
Product Code:  MEMO/301/1508.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471385 
eBook ISBN:  9781470479527 
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 DetailsMemoirs of the American Mathematical SocietyVolume: 301; 2024; 102 ppMSC: Primary 19

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 HesselholtMadsen $\mathbb {T}$Tate spectral sequence

14. Comparison of the HesselholtMadsen and Greenlees $\mathbb {T}$Tate Spectral Sequences

15. Coherence of the equivalences $E\mathbb {T}/E\mathbb {T}_{2n1}\simeq E\mathbb {T}_{+}\wedge S^{\mathbb {C}(1)^{n}}$ (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)


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Volume: 301; 2024; 102 pp
MSC: Primary 19

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 HesselholtMadsen $\mathbb {T}$Tate spectral sequence

14. Comparison of the HesselholtMadsen and Greenlees $\mathbb {T}$Tate Spectral Sequences

15. Coherence of the equivalences $E\mathbb {T}/E\mathbb {T}_{2n1}\simeq E\mathbb {T}_{+}\wedge S^{\mathbb {C}(1)^{n}}$ (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)
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