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Ted Chinburg and Matthew Stover
Small generators for S-unit groups of division algebras view print
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| Published: |
December 1, 2014
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| Keywords: |
Division algebras, S-unit groups, S-arithmetic lattices, heights on algebras, generators for S-unit groups, geometry of numbers |
| Subject: |
17A35, 20H10, 22E40, 11F06, 16H10, 16U60, 20F05, 11H06 |
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Abstract
Let k be a number field, suppose that B is a central simple division algebra over k, and choose any maximal order D of B. The object of this paper is to show that the group DS* of S-units of B is generated by elements of small height once S contains an explicit finite set of places of k. This generalizes a theorem of H. W. Lenstra, Jr., who proved such a result when B = k. Our height bound is an explicit function of the number field and the discriminant of a maximal order in B used to define its S-units.
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| Acknowledgements
Chinburg partially supported by NSF Grant DMS 1100355.
Stover partially supported by NSF RTG grant DMS 0602191 and NSF grant DMS 1361000.
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| Author information
Ted Chinburg:
Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 10104
ted@math.upenn.edu
Matthew Stover:
Department of Mathematics, Temple University, 1805 N. Broad Street, Philadelphia, PA 19122
mstover@temple.edu
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