Related papers: Maximal immediate extensions of valued differentia…

Over a global field any finite number of central simple algebras of exponent dividing $m$ is split by a common cyclic field extension of degree $m$. We show that the same property holds for function fields of two-dimensional excellent…

We discuss the massive extension of the four-dimensional superfield QED. For this theory, we calculate the one-loop effective potential of the chiral matter.

We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…

We study function fields of curves over a base field $K$ which is either a global field or a large field having a separable field extension of degree divisible by $4$. We show that, for any such function field, Hilbert's 10th Problem has a…

We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret's result about the ideal class group problem. Another is a…

Let $k$ be any field and $k^s$ its separable closure. Let $X$ be an affine variety over $k$ which is isomorphic to affine $n$-space over the field extension $k^s$. Then $X$ is isomorphic to affine $n$ space over $k$.

We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…

We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We deduce a classification of any Galois cubic extension of a…

In this paper we introduce a new invariant (the distant degree) for difference field extensions of finite transcendence degree, and we explore some of its properties. We also discuss a generalisation of this invariant and of the limit…

We answer two open questions about the model theory of valued differential fields introduced by Scanlon. We show that they eliminate imaginaries in the geometric language introduced by Haskell, Hrushovski and Macpherson and that they have…

We prove that the derived direct image of the constant sheaf with field coefficients under any proper map with smooth source contains a canonical summand. This summand, which we call the geometric extension, only depends on the generic…

Let $K$ be a complete discrete valued field of characteristic $p$ with residue $k$ which is not necessarily perfect. We prove the Conjecture in \cite{cs} that a $p$-algebra over $K$ contains a totally ramified cyclic maximal subfield if it…

Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski, where he obtains local…

A henselian valued field $K$ is called separably tame if its separable-algebraic closure $K^{\operatorname{sep}}$ is a tame extension, that is, the ramification field of the normal extension $K^{\operatorname{sep}}|K$ is…

We axiomatize a class of existentially closed exponential fields equipped with an $E$-derivation. We apply our results to the field of real numbers endowed with $exp(x)$ the classical exponential function defined by its power series…

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The…

Conformal symmetry is taken as an attribute of theories of massless fields in manifolds with specific dimensionalities. This paper shows that this is not an absolute truth; it is a consequence of the mathematical representation used for the…

The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to…

This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental…