On the Blumberg–Mandell Künneth theorem for \(\mathrm {TP}\)

Abstract

We give a new proof of the recent Künneth theorem for periodic topological cyclic homology of smooth and proper dg categories over perfect fields of characteristic \(p>0\) due to Blumberg and Mandell. Our result is slightly stronger and implies a finiteness theorem for topological cyclic homology of such categories.

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Correspondence to Benjamin Antieau.

Additional information

Benjamin Antieau was supported by NSF Grant DMS-1552766. Akhil Mathew was supported by a Clay Research Fellowship.

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Antieau, B., Mathew, A. & Nikolaus, T. On the Blumberg–Mandell Künneth theorem for \(\mathrm {TP}\). Sel. Math. New Ser. 24, 4555–4576 (2018). https://doi.org/10.1007/s00029-018-0427-x

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Keywords

  • Künneth theorems
  • The Tate construction
  • Topological Hochschild homology
  • Periodic topological cyclic homology

Mathematics Subject Classification

  • 14F30
  • 16E40
  • 19D55