Related papers: The domination monoid in henselian valued fields

Classically, Groebner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build…

We consider four properties of a field $K$ related to the existence of (definable) henselian valuations on $K$ and on elementarily equivalent fields, and study the implications between them. Surprisingly, the full pictures look very…

After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…

We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…

We show that any theory of tame henselian valued fields is NIP if and only if the theory of its residue field and the theory of its value group are NIP. Moreover, we show that if $(K,v)$ is a henselian valued field of residue characteristic…

Faltings proved that there are finitely many abelian varieties of genus $g$ over a number field $K$, with good reduction outside a finite set of primes $S$. Fixing one of these abelian varieties $A$, we prove that there are finitely many…

We introduce a new method of constructing complete sequences of key polynomials for simple extensions of tame fields. In our approach the key polynomials are taken to be the minimal polynomials over the base field of suitably constructed…

In this paper, we extend the theory of minimal limit key polynomials of valuations on the polynomial ring $\kx$. We use the theory of cuts on ordered abelian groups to show that the previous results on bounded sets of key polynomials of…

Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and $|\{p\text{ prime}:[G:pG]=\infty\}|<\infty$. We apply this to show that if $K$ is a strongly dependent field, then $(K,v)$…

We study metric valued fields in continuous logic, following Ben Yaacov's approach, thus working in the metric space given by the projective line. As our main result, we obtain an approximate Ax-Kochen-Ershov principle in this framework,…

In their article about distality in valued fields, Aschenbrenner, Chernikov, Gehret and Ziegler proved resplendent Ax-Kochen-Ershov principles for quantifier elimination in pure short exact sequences of Abelian structures. We study how…

We give a detailed analysis of the semisimple elements, in the sense of Vinberg, of the third exterior power of a 9-dimensional vector space over an algebraically closed field of characteristic different from 2 and 3. To a general such…

We establish relative quantifier elimination for valued fields of residue characteristic zero enriched with a non-surjective valued field endomorphism, building on recent work of Dor and Halevi. In particular, we deduce relative quantifier…

A new tool for the model theory of differentially closed fields and of compact complex manifolds is here developed. In such settings, it is shown that a type internal to the field of constants (resp. to the projective line) admits a maximal…

We develop a notion of a `canonical $\mathcal{C}$-henselian valuation' for a class $\mathcal{C}$ of field extensions, generalizing the construction of the canonical henselian valuation of a field. We use this to show that the $p$-adic…

Motivated by the theory of domination for types, we introduce a notion of domination for Keisler measures called extension domination. We argue that this variant of domination behaves similarly to its type setting counterpart. We prove that…

Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…

Two analytic examples of globally regular non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory in (3+1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang-Mills field…

We prove the existence of definable retractions onto arbitrary closed subsets of $K^{n}$ definable over Henselian valued fields $K$. Hence directly follows non-Archimedian analogues of the Tietze--Urysohn and Dugundji theorems on extending…

Let $(K,v)$ be a henselian valued field. Let $\mathbb{P}^{dless}\subset K[x]$ be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation $\,\approx\,$ on…