The Discriminant of an Algebraic Torus
arXiv:1105.3938 · doi:10.1016/j.jnt.2011.03.001
Abstract
For a torus T defined over a global field K, we revisit an analytic class number formula obtained by Shyr in the 1970's as a generalization of Dirichlet's class number formula. We prove a local-global presentation of the quasi-discriminant of T, which enters into this formula, in terms of cocharacters of T. This presentation can serve as a more natural definition of this invariant.
17 pages