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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year


IMPACT FACTOR increased in 2014: 1.432
Rank 22 out of 310 in category Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 3.585
Source Normalized Impact per Paper (SNIP) 2014: 1.745
Impact per Publication (IPP) 2014: 1.262

Mathematical Citation Quotient (MCQ) 2014: 1.27

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Non-archimedean amoebas and tropical varieties

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2006, Issue 601, Pages 139–157, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2006.097, February 2007

Publication History

Received:
2005-08-24
Revised:
2005-11-21
Published Online:
2007-02-12

Abstract

We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For hypersurfaces this set is also the negative of the tropical variety of the defining polynomial. Using non-archimedean analysis and a recent result of Conrad we prove that the amoeba of an irreducible variety is connected. We introduce the notion of an adelic amoeba for varieties over global fields, and establish a form of the local-global principle for them. This principle is used to explain the calculation of the non-expansive set for a related dynamical system.

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