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ON TORSION OF CLASS GROUPS OF CM TORI

Part of: Algebraic number theory: global fields Linear algebraic groups and related topics

Published online by Cambridge University Press:  28 March 2012

Christopher Daw
Christopher Daw*
Affiliation:
University College London, Department of Mathematics, Gower Street, London WC1E 6BT, U.K. (email: c.daw@ucl.ac.uk)
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Abstract

Let T be an algebraic torus over ℚ such that T(ℝ) is compact. Assuming the generalized Riemann hypothesis, we give a lower bound for the size of the class group of T modulo its n-torsion in terms of a small power of the discriminant of the splitting field of T. As a corollary, we obtain an upper bound on the n-torsion in that class group. This generalizes known results on the structure of class groups of complex multiplication fields.

MSC classification

Secondary: 11R29: Class numbers, class groups, discriminants 20G30: Linear algebraic groups over global fields and their integers 20G35: Linear algebraic groups over adèles and other rings and schemes
Type
Research Article
Information
Mathematika , Volume 58 , Issue 2 , July 2012 , pp. 305 - 318
Copyright
Copyright © University College London 2012

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