Reference : On Farrell-Tate cohomology of SL_2 over S-integers |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/28814 | |||

On Farrell-Tate cohomology of SL_2 over S-integers | |

English | |

Rahm, Alexander [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Wendt, Matthias [Universitaet Duisburg-Essen > Mathematics] | |

Oct-2018 | |

Journal of Algebra | |

Academic Press | |

512 | |

427-464 | |

Yes (verified by ORBi^{lu}) | |

International | |

0021-8693 | |

1090-266X | |

[en] In this paper, we provide number-theoretic formulas for Farrell–Tate cohomology for SL_2 over rings of S-integers in number fields satisfying a weak regularity assumption. These formulas describe group cohomology above the virtual cohomological dimension, and can be used to study some questions in homology of linear groups.
We expose three applications, to (I) detection questions for the Quillen conjecture, (II) the existence of transfers for the Friedlander–Milnor conjecture, (III) cohomology of SL_2 over number fields. | |

Gabor Wiese's University of Luxembourg grant AMFOR, De Brún Center for Computational Algebra at NUI Galway | |

Researchers ; Professionals | |

http://hdl.handle.net/10993/28814 | |

10.1016/j.jalgebra.2018.06.031 |

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