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A Rigidity Property for the Set of all Characters Induced by Valuations

Robert Bieri and John R. J. Groves
Transactions of the American Mathematical Society
Vol. 294, No. 2 (Apr., 1986), pp. 425-434
DOI: 10.2307/2000191
Stable URL: http://www.jstor.org/stable/2000191
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Rigidity Property for the Set of all Characters Induced by Valuations
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Abstract

If K is a field and G a finitely generated multiplicative subgroup of K then every real valuation on K induces a character G → R. It is known that the set $\Delta(G) \subseteq R^n$ of all characters induced by valuations is polyhedral. We prove that Δ(G) satisfies a certain rigidity property and apply this to give a new and conceptual proof of the Brewster-Roseblade result [4] on the group of automorphisms of K stabilizing G.

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