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The Slice Spectral Sequence of a $C_4$-Equivariant Height-4 Lubin–Tate Theory
About this Title
Michael A. Hill, XiaoLin Danny Shi, Guozhen Wang and Zhouli Xu
Publication: Memoirs of the American Mathematical Society
Publication Year:
2023; Volume 288, Number 1429
ISBNs: 978-1-4704-7468-3 (print); 978-1-4704-7571-0 (online)
DOI: https://doi.org/10.1090/memo/1429
Published electronically: August 2, 2023
Table of Contents
Chapters
- 1. Introduction
- 2. Preliminaries
- 3. The slice spectral sequence of $BP^{(\!(C_{4})\!)}\langle 1 \rangle$
- 4. The slice filtration of $BP^{(\!(C_{4})\!)}\langle 2 \rangle$
- 5. The $C_2$-slice spectral sequence of $i_{C_2}^* BP^{(\!(C_{4})\!)}\langle 2 \rangle$
- 6. Induced differentials from $BP^{(\!(C_{4})\!)}\!\langle 1 \rangle$
- 7. Higher differentials I: $d_{13}$ and $d_{15}$-differentials
- 8. Higher Differentials II: the Norm
- 9. Higher Differentials III: The Vanishing Theorem
- 10. Higher differentials IV: Everything until the $E_{29}$-page
- 11. Higher differentials V: $d_{29}$-differentials and $d_{31}$-differentials
- 12. Higher differentials VI: $d_{35}$ to $d_{61}$-differentials
- 13. Summary of Differentials
Abstract
We completely compute the slice spectral sequence of the $C_4$-spectrum $BP^{(\!(C_4)\!)}\langle 2 \rangle$. This spectrum provides a model for a height-4 Lubin–Tate theory with a $C_4$-action induced from the Goerss–Hopkins–Miller theorem. In particular, our computation shows that $E_4^{hC_{12}}$ is 384-periodic.- Shôrô Araki, Orientations in $\tau$-cohomology theories, Japan. J. Math. (N.S.) 5 (1979), no. 2, 403–430. MR 614829, DOI 10.4099/math1924.5.403
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