Related papers: A closedness theorem over Henselian valued fields …

We use a category-theoretic formulation of Aczel's Fullness Axiom from Constructive Set Theory to derive the local cartesian closure of an exact completion. As an application, we prove that such a formulation is valid in the homotopy…

The $\text{PSL}(4,\mathbb{R})$ Hitchin component of a closed surface group $\pi_1(S)$ consists of holonomies of properly convex foliated projective structures on the unit tangent bundle of $S$. We prove that the leaves of the…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.

We study the closure of the unitary orbit of a given point in the non-commutative Choquet boundary of a unital operator space with respect to the topology of pointwise norm convergence. This may be described more extensively as the…

We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.

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…

On a real ($\mathbb F=\mathbb R$) or complex ($\mathbb F=\mathbb C$) analytic connected 2-manifold $M$ with empty boundary consider two vector fields $X,Y$. We say that $Y$ {\it tracks} $X$ if $[Y,X]=fX$ for some continuous function…

Menger conjectured that subsets of $\mathbb R$ with the Menger property must be $\sigma$-compact. While this is false when there is no restriction on the subsets of $\mathbb R$, for projective subsets it is known to follow from the Axiom of…

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.

We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…

Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no…

A main purpose of this paper is to prove that the class of finite dimensional algebras which verify Han's conjecture is closed under split bounded extensions.

There exists a function f: N -> N such that for every positive integer d, every quasi-finite field K and every projective hypersurface X of degree d and dimension at least f(d), the set X(K) is non-empty. This is a special case of a more…

Let $(K, v)$ be a Henselian discrete valued field with a quasifinite residue field. This paper proves the existence of an algebraic extension $E/K$ satisfying the following: (i) $E$ has dimension dim$(E) \le 1$, i.e. the Brauer group Br$(E…

Generic absoluteness is the phenomenon that certain truths in the set-theoretic universe remain stable under forcing expansions. A classical result by Kripke asserts that every complete Boolean algebra completely embeds into a countably…

We prove that NIP valued fields of positive characteristic are henselian. Furthermore, we partially generalize the known results on dp-minimal fields to dp-finite fields. We prove a dichotomy: if K is a sufficiently saturated dp-finite…

The concept of a skew root of a skew polynomial is used to introduce notions of algebraic closedness for $\sigma$-fields, that is, a field equipped with an endomorphism. It is shown that every $\sigma$-field can be embedded in algebraically…

We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…

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…

The purpose of this short note is to study dominant rational maps from punctual Hilbert schemes of length $k>1$ of projective K3 surfaces $S$ containing infinitely many rational curves. Precisely, we prove that their image is necessarily…