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The discriminant of an algebraic torus |
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| Authors: | Rony A. Bitan |
| Affiliation: | Department of Mathematics, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel |
| Abstract: | For a torus T defined over a global field K, we revisit an analytic class number formula obtained by Shyr in the 1970s 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. |
| Keywords: | Algebraic groups Algebraic torus Global field Local field Discriminant Galois modules Class number Character group Cocharacter group Tamagawa measure Shyr?s invariant |
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