## Abstract

We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava E-theory, H^{∗}(G2, Et), at p = 2, for 0 ≤ t < 12, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the d3-differentials in the homotopy fixed point spectral sequence for the K(2)-local sphere spectrum. These cohomology groups and differentials play a central role in K(2)-local stable homotopy theory.

Original language | English (US) |
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Pages (from-to) | 1761-1805 |

Number of pages | 45 |

Journal | Transactions of the American Mathematical Society |

Volume | 377 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2024 |

### Funding

Received by the editors February 22, 2023, and, in revised form, April 30, 2023. 2020 Mathematics Subject Classification. Primary 55P42. This material is based upon work supported by the National Science Foundation under grants No. DMS-2005627, DMS-1906227 and DMS-1812122. A large portion of this work was conducted at the Max Planck Institute for Mathematics in Bonn and the authors would like to thank the MPIM for the hospitality. The authors would also like to thank the Hausdorff Research Institute for Mathematics for the hospitality in the context of the Trimester program Spectral Methods in Algebra, Geometry, and Topology, funded by the Deutsche Forschungs-gemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics