Brauer groups of torsors under algebraic tori

Abstract

Let $T$ be an algebraic torus defined over a global field $K$. For any $K$-torsor $X$ under $T$, we relate the Brauer group of $X$ to the adéle class group of $T$ as well as to the Shafarevich Tate group of $T$.

arXiv comment13 pages; Revised and updated