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Uniqueness of \(\textit{BP} \langle {n} \rangle \)

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Abstract

Fix a prime number p and an integer \(n \ge 0\). We prove that if a p-complete spectrum X satisfying a mild finiteness condition has the same mod p cohomology as \(\textit{BP} \langle {n} \rangle \) as a module over the Steenrod algebra, then X is weak homotopy equivalent to the p-completion of \(\textit{BP}\langle {n} \rangle \).

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Acknowledgments

The authors would like to thank Craig Westerland for many helpful conversations. Without him we would not have started thinking about twisted \(\textit{BP} \langle {n} \rangle \)-cohomology and we would not have been led to the main result of this paper. The first author was supported by an ARC Discovery grant. The second author was partially supported by the DFG through SFB-1085, and thanks the Australian National University for hosting him while this research was conducted.

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Correspondence to Vigleik Angeltveit.

Additional information

Communicated by Mark Behrens.

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Angeltveit, V., Lind, J.A. Uniqueness of \(\textit{BP} \langle {n} \rangle \) . J. Homotopy Relat. Struct. 12, 17–30 (2017). https://doi.org/10.1007/s40062-015-0120-0

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Keywords

  • Complex cobordism
  • Brown–Peterson spectrum
  • Adams spectral sequence