The Discriminant of an Algebraic Torus

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

References in corpus (3)

• A guide to the reduction modulo p of Shimura varieties
• On parahoric subgroups
• Chevalley's ambiguous class number formula for an arbitrary torus

Cited by in corpus (6)

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• On the cohomology of tori over local fields with perfect residue field
• A building-theoretic approach to relative Tamagawa numbers of quasi-split semisimple groups over global function fields