The Discriminant of an Algebraic Torus
Algebraic Geometry
2011-05-20 v1
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.
Cite
@article{arxiv.1105.3938,
title = {The Discriminant of an Algebraic Torus},
author = {R. A. Bitan},
journal= {arXiv preprint arXiv:1105.3938},
year = {2011}
}
Comments
17 pages