Related papers: Some properties of analytic difference fields
We give a universal property of the construction of the ring of $p$-typical Witt vectors of a commutative ring, endowed with Witt vectors Frobenius and Verschiebung, and generalize this construction to the derived setting. We define an…
The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations…
We present an axiomatic approach to combination theorems for various homological properties of groups and, more generally, of chain complexes. Examples of such properties include algebraic finiteness properties, $\ell^2$-invisibility,…
We reformulate several basic notions of notions in finite group theory in terms of iterations of the lifting property (orthogonality) with respect to particular morphisms. Our examples include the notions being nilpotent, solvable, perfect,…
We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their $n$-point functions…
This paper is a sequel to [1] and considers definability in differential-henselian monotone fields with c-map and angular component map. We prove an Equivalence Theorem among whose consequences are a relative quantifier reduction and an NIP…
Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…
We introduce an abstract framework to study certain classes of stably embedded pairs of models of a complete $\mathcal{L}$-theory $T$, called \textit{beautiful pairs}, which comprises Poizat's belles paires of stable structures and van den…
Imposing Huygens' Principle in a 4D Wightman QFT puts strong constraints on its algebraic and analytic structure. These are best understood in terms of ``biharmonic fields'', whose properties reflect the presence of infinitely many…
If $A$ is a finite-dimensional algebra graded by a group $G$, and $\sigma \in G$, we define a variant of paratrophic matrix associated with $A$ and $\sigma$, and we use it to characterize the $\sigma$-graded Frobenius property for $A$. We…
We prove that the class of partial differential fields of characteristic zero with an automorphism has a model companion. We then establish the basic model theoretic properties of this theory and prove that it satisfies the Zilber dichotomy…
By using help of algebraic operad theory, Leibniz algebra theory and symplectic-Poisson geometry are connected. We introduce the notion of cohomological vector field defined on nongraded symplectic plane. It will be proved that the…
Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…
We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian…
We consider associative algebras over a field of characteristic zero. We give a version of the proof of the Kemer's theorems concerning the Specht problem solution. It is proved that the ideal of graded identities of a finitely generated…
We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms…
We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…
Let G denote a connected, quasi-split reductive group over a field F that is complete with respect to a discrete valuation and that has a perfect residue field. Under mild hypotheses, we produce a subset of the Lie algebra g(F) that picks…
The derivation on the differential-valued field $\mathbb{T}_{\log}$ of logarithmic transseries induces on its value group $\Gamma_{\log}$ a certain map $\psi$. The structure $\Gamma = (\Gamma_{\log},\psi)$ is a divisible asymptotic couple.…
To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a…