Cohomology of adéle class groups of algebraic tori

Abstract

Let $T$ be an algebraic torus defined over a global field $K$ and split over a finite cyclic extension. In this paper, we determine the Herbrand quotient of the adéle class group of $T$. Our result can be seen as an extension of the so-called first inequality of global class field theory.

arXiv commentThis paper has been withdrawn because the main theorem is incorrect