The Strong Kunneth Theorem for Topological Periodic Cyclic Homology

Andrew J. Blumberg, Columbia University, New York, New York. Michael A. Mandell, Indiana University, Bloomington, Indiana.

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)