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Non-archimedean amoebas and tropical varieties

Identifieur interne : 000B53 ( Main/Merge ); précédent : 000B52; suivant : 000B54

Non-archimedean amoebas and tropical varieties

Auteurs : Manfred Einsiedler [États-Unis] ; Mikhail Kapranov [États-Unis] ; Douglas Lind [États-Unis]

Source :

Journal für die reine und angewandte Mathematik (Crelles Journal) [ 0075-4102 ] ; 2006-12-19.

RBID : ISTEX:4D60B1AC29A1A8AA9E2EC04F8FD3BF5FB53C6702

English descriptors

KwdEn :
- Adelic, Adelic amoeba, Algebra, Algebraic, Algebraic closure, Algebraic variety, Amoeba, Analytic space, Bernd sturmfels, Complex amoeba, Convex, Douglas lind, Einsiedler, Expansive, Expansive subdynamics, Formal laurent series, Grothendieck topology, Irreducible, Irreducible variety, Kapranov, Klaus schmidt, Laurent, Laurent series, Lind, Nite, Nite union, Nitely, Polyhedral, Polyhedron, Pure dimension, Radial projection, Reine angew, Sgen, Subset, Topology, Tropical geometry, Tropical varieties, Tropical variety.
Teeft :
- Adelic, Adelic amoeba, Algebra, Algebraic, Algebraic closure, Algebraic variety, Amoeba, Analytic space, Bernd sturmfels, Complex amoeba, Convex, Douglas lind, Einsiedler, Expansive, Expansive subdynamics, Formal laurent series, Grothendieck topology, Irreducible, Irreducible variety, Kapranov, Klaus schmidt, Laurent, Laurent series, Lind, Nite, Nite union, Nitely, Polyhedral, Polyhedron, Pure dimension, Radial projection, Reine angew, Sgen, Subset, Topology, Tropical geometry, Tropical varieties, Tropical variety.

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.

Url:

https://api.istex.fr/document/4D60B1AC29A1A8AA9E2EC04F8FD3BF5FB53C6702/fulltext/pdf

DOI: 10.1515/CRELLE.2006.097

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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Non-archimedean amoebas and tropical varieties

Non-archimedean amoebas and tropical varieties

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English descriptors

Abstract

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