Vanishing theorems and Brauer-Hasse-Noether exact sequences for higher-dimensional fields} \newcommand{\abstra}{When one wants to study the arithmetic of a given field $K$, it is often useful to understand the cohomology of the Galois module of roots of unity $\mathbb{Q}/\mathbb{Z}(1)$ or, more generally, the cohomology of its twists $\mathbb{Q}/\mathbb{Z}(r)$. In this talk, we will be interested in the situation when $K$ is a finite extension of the Laurent series field in $m$ variables $k((x_1, ..., x_m))$ with coefficients in a finite field, a $p$-adic field or a number field. We will discuss some vanishing theorems as well as some exact sequences that play the role of the Brauer-Hasse-Noether exact sequence for the field $K$.
Freitag, den 16. November 2018 um 13.30 Uhr, in INF 205, SR A Freitag, den 16. November 2018 at 13.30, in INF 205, SR A
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Alexander Schmidt