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Commensurability of automorphism groups

Part of: Abelian categories Algebraic number theory: global fields Division rings and semisimple Artin rings

Published online by Cambridge University Press:  06 February 2017

Alex Bartel  and
Hendrik W. Lenstra Jr.
Alex Bartel
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK
Hendrik W. Lenstra Jr.
Affiliation:
Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, The Netherlands
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Abstract

We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen–Lenstra heuristics on class groups.

Keywords

calculus of fractionsCohen–Lenstra heuristicscommensurabilityring isogeniessemisimple rings

MSC classification

Primary: 11R29: Class numbers, class groups, discriminants 16H20: Lattices over orders 16K20: Finite-dimensional 18E35: Localization of categories
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 2 , February 2017 , pp. 323 - 346
Copyright
© The Authors 2017 

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