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T -filtres, ensembles analytiques et transformation de Fourier P -adique

Alain Escassut (1975)

Annales de l'institut Fourier

Les propriétés des éléments analytiques sur une partie D d’un corps ultramétrique complet, algébriquement clos, dépendent de l’existence sur D de filtres strictement annulateurs que l’on caractérise par des relations arithmétiques entre les diamètres et les distances mutuelles des trous de D grâce à la notion de T -filtre. Alors les ensembles analytiques sont les ensembles sans T -filtre à plage non vide. D’autre part, le problème de la transformation de Fourier p -adique se ramène à un problème d’analycité...

The Joly–Becker theorem for * –orderings

Igor Klep, Dejan Velušček (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the * –version of the Joly–Becker theorem: a skew field admits a * –ordering of level n iff it admits a * –ordering of level n ℓ for some (resp. all) odd ℓ ∈ ℕ . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a * –ordering of higher level also admits a * –ordering of level 1 . Every field that admits a * –ordering of higher level admits a * –ordering of level 1 or 2

The moduli space of n tropically collinear points in Rd.

Mike Develin (2005)

Collectanea Mathematica

The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension...

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