The discriminant of an algebraic torus

Rony A. Bitan

doi:10.1016/j.jnt.2011.03.001

The discriminant of an algebraic torus

Rony A. Bitan

Technion-Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	1657-1671
Number of pages	15
Journal	Journal of Number Theory
Volume	131
Issue number	9
DOIs	https://doi.org/10.1016/j.jnt.2011.03.001
State	Published - Sep 2011
Externally published	Yes

Bibliographical note

Funding Information:
Partially supported by the ISF center of excellency grant 1438/06.

Funding

Partially supported by the ISF center of excellency grant 1438/06.

Funders	Funder number
ISF Center of Excellency	1438/06

Keywords

Algebraic groups
Algebraic torus
Character group
Class number
Cocharacter group
Discriminant
Galois modules
Global field
Local field
Shyr's invariant
Tamagawa measure

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10.1016/j.jnt.2011.03.001

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keywords = "Algebraic groups, Algebraic torus, Character group, Class number, Cocharacter group, Discriminant, Galois modules, Global field, Local field, Shyr's invariant, Tamagawa measure",

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KW - Algebraic groups

KW - Algebraic torus

KW - Character group

KW - Class number

KW - Cocharacter group

KW - Discriminant

KW - Galois modules

KW - Global field

KW - Local field

KW - Shyr's invariant

KW - Tamagawa measure

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JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 9

ER -

The discriminant of an algebraic torus

Abstract

Bibliographical note

Funding

Keywords

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