### SoSe 21 Oberseminar: Hermitian K-theory of rings

**Time and place:** Tuesday 14:15-15:45 online

The goal of this seminar is to study some recent developments on the Hermitian K-theory of rings of integers following Calmès, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus, and Steimle. A particular focus will be on the complete solution of Thomason’s homotopy limit problem for number rings, which states that the Grothendieck–Witt spectrum of a number ring is 2-adically equivalent to the homotopy C₂-fixed points of its K-theory spectrum. In particular we will review the solution of this problem for fields using motivic homotopy techniques, following Bachmann and Hopkins.

The main references are:

*Hermitian K-theory for stable ∞-categories III: Grothendieck–Witt groups of rings**η-periodic motivic stable homotopy theory over fields*(Appendix A and references therein)

Date | Speaker | Topic |
---|---|---|

27.04 | Marc Hoyois | Introduction |

04.05 | Niklas Kipp | The homotopy t-structure on motivic spectra |

11.05 | Pavel Sechin | The motivic Hermitian K-theory spectrum |

18.05 | Denis Nardin | Voevodsky’s slice filtration and Levine’s coniveau filtration |

25.05 | Tom Bachmann | The convergence of the slice filtration |

01.06 | — | — |

08.06 | Marc Hoyois | The slices of Hermitian K-theory and the homotopy limit problem away from 2 |

15.06 | Luca Pol | Algebraic surgery |

22.06 | Lucy Yang | Regular coherent rings |

29.06 | Elden Elmanto | Dévissage in Hermitian K-theory and the localization sequence |

06.07 | Denis Nardin | The homotopy limit problem for rings of integers |