Joint IAS/PU Number Theory Seminar | |

Topic: | Local Global Principles for Galois Cohomology |

Speaker: | Julia Hartmann |

Affiliation: | RWTH Aachen University; Member, School of Mathematics |

Date: | Thursday, December 13 |

Time/Room: | 4:30pm - 5:30pm/S-101 |

Video Link: | https://video.ias.edu/1213/members/1213-JuliaHartmann |

We consider Galois cohomology groups over function fields F of curves that are defined over a complete discretely valued field. Motivated by work of Kato and others for n=3, we show that local-global principles hold for H^n(F, Z/mZ(n-1)) for all n>1. In the case n=1, a local-global principle need not hold. Instead, we will see that the obstruction to a local-global principle for H^1(F,G), a Tate-Shafarevich set, can be described explicitly for many (not necessarily abelian) linear algebraic groups G. Concrete applications of the results include central simple algebras and Albert algebras.