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A 'Non-Additive' Characterization of p-Adic Norms
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
2011 (English)In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 15, no 1, 37-50 p.Article in journal (Refereed) Published
Abstract [en]

For F a p-adic field together with a p-adic valuation, we present a new characterization for a map p: F-n -> R boolean OR {-infinity} to be a delta-adic norm on the vector space F-n. This characterization was motivated by the concept of tight maps-maps that naturally arise within the theory of valuated matroids and tight spans. As an immediate consequence, we show that the two descriptions of the affine building of SLn(F) in terms of (i) p-adic norms given by Bruhat and Tits and (ii) tight maps given by Terhalle essentially coincide. The result suggests that similar characterizations of affine buildings of other classical groups should exist, and that the theory of affine buildings may turn out as a particular case of a yet to be developed geometric theory of valuated (and delta-valuated) matroids and their tight spans providing simply-connected G-spaces for large classes of appropriately specified groups G that could serve as a basis for an affine variant of Gromov's theory.

Place, publisher, year, edition, pages
2011. Vol. 15, no 1, 37-50 p.
Keyword [en]
buildings, affine buildings, p-adic norms, tropical geometry of Grassmann-Plucker varieties, matroids, valuated matroids, tight span
National Category
URN: urn:nbn:se:uu:diva-156157DOI: 10.1007/s00026-011-0081-xISI: 000292037800003OAI: oai:DiVA.org:uu-156157DiVA: diva2:430878
Available from: 2011-07-13 Created: 2011-07-12 Last updated: 2012-02-16Bibliographically approved

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Algebra, Geometry and Logic
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