## Abstract

We introduce a computationally tractable way to describe the Z-homotopy fixed points of a C_{n}-spectrum E, producing a genuine Cn spectrum E^{hnZ} whose fixed and homotopy fixed points agree and are the Z-homotopy fixed points of E. These form the bottom piece of a contravariant functor from the divisor poset of n to genuine C_{n}-spectra, and when E is an N_{∞}-ring spectrum, this functor lifts to a functor of N_{∞}-ring spectra. For spectra like the Real Johnson-Wilson theories or the norms of Real bordism, the slice spectral sequence provides a way to easily compute the RO(G)-graded homotopy groups of the spectrum E^{hnZ}, giving the homotopy groups of the Z-homotopy fixed points. For the more general spectra in the contravariant functor, the slice spectral sequences interpolate between the one for the norm of Real bordism and the especially simple Z-homotopy fixed point case, giving us a family of new tools to simplify slice computations.

Original language | English (US) |
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Pages (from-to) | 92-115 |

Number of pages | 24 |

Journal | New York Journal of Mathematics |

Volume | 26 |

State | Published - 2020 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2020, University at Albany. All rights reserved.

## Keywords

- Equivariant homotopy
- Homotopy fixed points
- Slice spectral sequence

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