The intersection of valuation rings
The Joly–Becker theorem for –orderings
We prove the –version of the Joly–Becker theorem: a skew field admits a –ordering of level iff it admits a –ordering of level for some (resp. all) odd . 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 . Every field that admits a –ordering of higher level admits a –ordering of level or
The limit behaviour of exponential terms
The moduli space of n tropically collinear points in Rd.
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...
The Newton polygon of a product of power series.
The non-archimedean Corona problem
The norm of uniform convergence on the -algebraic maximal spectrum of an algebra over a non-archimedean valuation field
The number of zeros of polynomials in valuation rings of complete discretely valued fields
The quadratic form transfer and valuations.
The Relative Separable Closure of a Valued Field in its Completion.
The representation of one quadratic form by another in valuated fields
The Set of Derivatives in a Non-Archimedean Field.
The structure of ideals in the Banach algebra of Lipschitz functions over valued fields
The tropical Grassmannian.
Théorie algébrique de la croissance
Théorie de Baire -adique
Topological algebras of continuous functions over valued fields
Topologies de corps A-linéaires
Topologische Charakterisierung globaler Körper und algebraischer Funktionenkörper in einer Variablen.
Topology on ordered fields
An ordered field is a field which has a linear order and the order topology by this order. For a subfield of an ordered field, we give characterizations for to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on .