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Strong Kunneth Theorem for Topological Periodic Cyclic Homology

Blumberg, Andrew J. Mandell Michael A.
Heftet / 2024 / Engelsk

Produktdetaljer

ISBN
9781470471385
Publisert
2024-10-20
Utgiver
Vendor
American Mathematical Society
Høyde
254 mm
Bredde
178 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
102

Forfatter
Blumberg, Andrew J.
Mandell Michael A.

Biografisk notat

Andrew J. Blumberg, Columbia University, New York, New York.

Michael A. Mandell, Indiana University, Bloomington, Indiana.

Strong Kunneth Theorem for Topological Periodic Cyclic Homology

Blumberg, Andrew J. Mandell Michael A.
Heftet / 2024 / Engelsk
Blumberg, Andrew J. Mandell Michael A.
Heftet / 2024 / Engelsk
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  • 1. Introduction
  • 2. Orthogonal $G$-spectra and the Tate fixed points
  • 3. A lax Kunneth 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 Kunneth 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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Relaterte produkter

  • 1. Introduction
  • 2. Orthogonal $G$-spectra and the Tate fixed points
  • 3. A lax Kunneth 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 Kunneth 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)
Les mer

Produktdetaljer

ISBN
9781470471385
Publisert
2024-10-20
Utgiver
Vendor
American Mathematical Society
Høyde
254 mm
Bredde
178 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
102

Forfatter
Blumberg, Andrew J.
Mandell Michael A.

Biografisk notat

Andrew J. Blumberg, Columbia University, New York, New York.

Michael A. Mandell, Indiana University, Bloomington, Indiana.

Relaterte produkter