caa a22 4500 445855460 CHVBK 20180317145426.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00026-011-0081-x doi (NATIONALLICENCE)springer-10.1007/s00026-011-0081-x A ‘Non-Additive' Characterization of $${\wp}$$ -Adic Norms [Elektronische Daten] [A. Dress, J. Kåhrström, V. Moulton] For F a $${\wp}$$ -adic field together with a $${\wp}$$ -adic valuation, we present a new characterization for a map $${p: F^{n} \rightarrow {\mathbb R}\cup\{-\infty}\}$$ to be a $${\wp}$$ -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 SL n (F) in terms of (i) $${\wp}$$ -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 δ-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. Springer Basel AG, 2011 buildings nationallicence affine buildings nationallicence $${\wp}$$ -adic norms nationallicence tropical geometry of Grassmann-Plücker varieties nationallicence matroids nationallicence valuated matroids nationallicence tight span nationallicence Dress A. Department of Combinatorics and Geometry, CAS-MPG Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai, China aut Kåhrström J. Department of Mathematics, Uppsala University, BMC, Box 598, 751 24, Uppsala, Sweden aut Moulton V. School of Computing Sciences, University of East Anglia, NR4 7TJ, Norwich, UK aut Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 37-50 0218-0006 15:1<37 2011 15 26 https://doi.org/10.1007/s00026-011-0081-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0081-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dress A. Department of Combinatorics and Geometry, CAS-MPG Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai, China aut NATIONALLICENCE 700 1- Kåhrström J. Department of Mathematics, Uppsala University, BMC, Box 598, 751 24, Uppsala, Sweden aut NATIONALLICENCE 700 1- Moulton V. School of Computing Sciences, University of East Anglia, NR4 7TJ, Norwich, UK aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 37-50 0218-0006 15:1<37 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer