Jump to ContentJump to Main Navigation

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

Increased IMPACT FACTOR 2013: 1.303
5-year IMPACT FACTOR: 1.427
Rank 21 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition
Mathematical Citation Quotient 2013: 1.32

VolumeIssuePage

Issues

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.

Comments (0)

Please log in or register to comment.
Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.