Related papers: Model theory of valued fields with an endomorphism

We prove in arbitrary characteristic that an immediate valued algebraic function field $F$ of transcendence degree 1 over a tame field $K$ is contained in the henselization of $K(x)$ for a suitably chosen $x\in F$. This eliminates…

This is an introduction to the author theory of cyclic p-extensions of an absolutely unramified complete discrete valuation field K with arbitrary residue field of characteristic p. In this theory a homomorphism is constructed from the…

There is a large class of classical null-fronted metrics in which a free scalar field has an infinite number of conservation laws. In particular, if the scalar field is quantized, the number of particles is conserved. However, with more…

We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central…

For a simply connected semisimple algebraic group over an algebraically closed field of positive characteristic we have already constructed a splitting of the Frobenius endomorphism on its algebra of distributions. We generalize the…

Let $F$ be a finite field of order $q$ and characteristic $p$. Let $\mathbb{Z}_F=F[t]$, $\mathbb{Q}_F=F(t)$, $\mathbb{R}_F=F((1/t))$ equipped with the discrete valuation for which $1/t$ is a uniformizer, and let…

Quasi-free endomorphisms of the CAR and CCR algebras are studied from the point of view of the theory of superselection sectors.

We study the model theory of deeply ramified fields of positive characteristic. Generalizing the perfect case treated in work by Jahnke and Kartas on the model theory of perfectoid fields, we obtain Ax-Kochen/Ershov principles for certain…

We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is a first-order sentence which characterizes this field within the class up to…

We prove that if $K$ is a complete algebraically closed non-archimedian valuation field of positive characteristic and $f$ is an endomorphism of $\mathbb{P}_{K}^{N}$ which is totally inseparable and behaves as the Frobenius on the special…

Let $T$ be a complete strongly geometric theory of fields with quantifier elimination. We show that the theory of lovely pairs of $T$ has quantifier elimination in Delon's definitional expansion by predicates for linear independence and…

Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…

These notes present Sobolev-Gagliardo-Nirenberg endpoint estimates for classes of homogeneous vector differential operators. Away of the endpoint cases, the classical Calder\'on-Zygmund estimates show that the ellipticity is necessary and…

The notion of newtonianity is central to the study of the ordered differential field of logarithmic-exponential transseries done by Aschenbrenner, van den Dries, and van der Hoeven; see Chapter 14 of arxiv:1509.02588. We remove the…

We prove through path integral Monte Carlo computer experiments that the affine quantization of the $\varphi_4^4$ scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well defined continuum…

Let $(K,\nu)$ be an arbitrary-rank valued field, $R_\nu$ its valuation ring, $K(\alpha)/K$ a separable finite field extension generated over $K$ by a root of a monic irreducible polynomial $f\in R_\nu[X]$. We give necessary and sufficient…

The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.

Using a local monomialization result of Knaf and Kuhlmann, we prove that the valuation ring of an Abhyankar valuation of a function field over a perfect ground field of prime characteristic is Frobenius split. We show that a Frobenius…

We study model-complete fields that avoid a given quasi-project variety $V$. There is a close connection between hyperbolicity of $V$ and the existence of the model companion for the theory of characteristic-zero fields avoiding rational…

We resolve an algebraic version of Schoenberg's celebrated theorem [Duke Math.J., 1942] characterizing entrywise matrix transforms that preserve positive definiteness. Compared to the classical real and complex settings, we consider…