-extremal valued fields.
A characterization of locally compact fields II
A characterization of locally compact fields, III
A characterization of locally compact fields of zero characteristic
A characterization of the spherically complete normed spaces with a distinguished basis
A continuous, constructive solution to Hilbert's 17th problem.
A generalization of Ostrowski' theorem on ultrametric inequalities.
A model-theoretic transfer theorem for henselian valued fields.
A non-archimedean “curve integral” and its application to the construction of potentials and solutions of differential equations
A note on Abhyankar-Moh's approximate roots of polynomials.
A note on linear preserves of ternary cubic forms
A p-adic behaviour of dynamical systems.
We study dynamical systems in the non-Archimedean number fields (i.e. fields with non-Archimedean valuation). The main results are obtained for the fields of p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter...
A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.
Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning...
A representation theorem for a class of rigid analytic functions
Let be a prime number, the field of -adic numbers and the completion of the algebraic closure of . In this paper we obtain a representation theorem for rigid analytic functions on which are equivariant with respect to the Galois group , where is a lipschitzian element of and denotes the -neighborhood of the -orbit of .
A spectral theorem for matrices over fields of power series
A weak Hasse principle for central simple algebras with an involution.
Abelian extensions of an absolutely unramified local field with general residue field.
Abhyankar places admit local uniformization in any characteristic
About -adic interpolation of continuous and differentiable functions
Absolute Galois Groups of p-Adically Maximal PpC Fields.