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Les amibesdes variétés algébriques dans ${(ℂ^{*})}^{n}$ sont les images de ces variétés par l’application des moments $Log : {(ℂ^{*})}^{n} \to ℝ^{n}$ , $Log : (z_{1}, ..., z_{n}) \mapsto (log | z_{1} |, ..., log | z_{n} |)$ . Des résultats obtenus par G. Mikhalkin montrent l’utilité des amibes pour l’étude des variétés algébriques réelles et complexes. Les amibes peuvent être déformées en des complexes polyédraux appelésvariétés algébriques tropicales. Cette déformation permet, en particulier, de calculer les invariants de Gromov-Witten du plan projectif et d’autres surfaces toriques en dénombrant des courbes...

An Algorithm for Lifting Points in a Tropical Variety

Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig (2008)

Collectanea Mathematica

An application of newton iteration procedure to $p$ -adic differential equations

Yasutaka Sibuya (1979/1981)

Groupe de travail d'analyse ultramétrique

An elementary identity in the theory of Hecke L-functions.

Uwe Weselmann (1989)

Inventiones mathematicae

An example of a locally unbounded complete extension of the p-adic number field

W. Więsław (1974)

Colloquium Mathematicae

An extension of approximation theorems

Jiři Močkoř (1975)

Colloquium Mathematicae

An isomorphism theorem for Henselian algebraic extensions of valued fields.

Serban A. Basarab, F.-V. Kuhlmann (1992)

Manuscripta mathematica

An $ℓ$ -algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem

Stuart A. Steinberg (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.

An ultrametric Nevanlinna’s second main theorem for small functions of a special type

Henna Jurvanen (2010)

Annales mathématiques Blaise Pascal

In ultrametric Nevanlinna theory, the Nevanlinna’s second main theorem for small functions has only been proved in the case of at most three small functions. In this paper, we prove a second main theorem for $q$ small functions of a special type when the residue characteristic of the field is zero.

Analyse $p$ -adique

Yvette Amice (1959/1960)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

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