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The Strong Künneth Theorem for Topological Periodic Cyclic Homology

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
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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Book DetailsMemoirs of the American Mathematical SocietyVolume: 301; 2024; 102 ppMSC: Primary 19
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Table of Contents
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Chapters
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1. Introduction
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2. Orthogonal $G$-spectra and the Tate fixed points
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3. A lax Künneth theorem for Tate fixed points
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4. The Tate spectral sequences
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5. Topological periodic cyclic homology
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6. A filtration argument (Proof of Theorem A)
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7. Filtered modules over filtered ring orthogonal spectra
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8. Comparison of the lefthand and righthand spectral sequences (Proof of Theorem 6.3)
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9. Conditional convergence of the lefthand spectral sequence (Proof of Lemma 6.5)
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10. Constructing the filtered model: The positive filtration
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11. Constructing the filtered model: The negative filtration
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12. Constructing the filtered model and verifying the hypotheses of Chapter 6
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13. The $E^1$-term of the Hesselholt-Madsen $\mathbb {T}$-Tate spectral sequence
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14. Comparison of the Hesselholt-Madsen and Greenlees $\mathbb {T}$-Tate Spectral Sequences
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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)
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16. The strong Künneth theorem for $THH$
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17. $THH$ of smooth and proper algebras (Proof of Theorem C)
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18. The finiteness theorem for $TP$ (Proof of Theorem B)
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19. Comparing monoidal models
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20. Identification of the enveloping algebras and $\operatorname {Bal}$
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21. A topologically enriched lax symmetric monoidal fibrant replacement functor for equivariant orthogonal spectra (Proof of Lemma 3.1)
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Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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 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
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