We present several results on the compactness of space morphisms between analytic spaces in sense Berkovich. show that under certain conditions source, every sequence maps having an affinoid target has a subsequence converges pointwise to continuous map. also study class arise this way. Locally, they turn be after base change. Our naturally lead definition normal families. give some application...

We prove non-archimedean analogue of Sendov’s conjecure. also provide complete list polynomials over an algebraically closed field $$K$$ that satisfy the optimal bound in conjecture.

An action for a prospect of $p$-adic open superstring on target Minkowski space is proposed. The constructed `worldsheet' fields taking values in the field $\mathbb{Q}_p$, but it assumed to be obtained from discrete Bruhat-Tits tree. This proven have an analog worldsheet supersymmetry and superspace also terms superfields. does not conformal symmetry, however implemented definition amplitudes. ...

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential for...

Throughout the history of physics a key tool in the development of physical laws has been the infinitesimal. Infinitesimals entered the scene with the development of the calculus by Newton and Leibniz and went on to be used, to mention some of the most notable cases, in Euler’s derivation of the laws of hydrodynamics, in the development of analytical mechanics by Euler, Lagrange and Hamilton an...

We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the naive height into an archimedean and a non-archimedean term. Our main contribution is an algorithm for the computation of the non-archimedean term that require...

Non-archimedean seminorms on rings and modules provide in general a structure which is richer than the associated linear topology [3], [2]. We want to characterize Banach spaces and commutative algebras over a complete non-trivially valued nonarchimedean field K, as linearly topologized modules over the ring of integers K◦ of K, with no reference to any specific norm. This is analog to the clas...