Related papers: Burden in Henselian Valued Fields

We derive a formula for the weight system of the multivariable Alexander polynomial using determinants, show that it obeys known relations, and satisfies some of the same relations as the single variable polynomial.

We introduce and analyse a class of weighted Sobolev spaces with mixed weights on angular domains. The weights are based on both the distance to the boundary and the distance to the one vertex of the domain. Moreover, we show how the…

The Alesker product turns the space of smooth translation-invariant valuations on convex bodies into a commutative associative unital algebra, satisfying Poincar\'e duality and the hard Lefschetz theorem. In this article, a version of the…

We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials.…

The notion of the weighted degree of a polynomial is a basic tool in Affine Algebraic Geometry. In this paper, we study the properties of the weighted multidegrees of polynomial automorphisms by a new approach which focuses on stable…

We determine the all-genus Hodge-Gromov-Witten theory of a smooth hypersurface in weighted projective space defined by a chain or loop polynomial. In particular, we obtain the first genus-zero computation of Gromov-Witten invariants for…

We present elements of a theory of translation-invariant integration, measure, and harmonic analysis on a valuation field with local field as residue field. This extends the work of Fesenko. Applications to zeta integrals for…

We discuss definability in the language of rings without parameters of the unique canonical henselian valuation of a field. We show that in most cases where the canonical henselian valuation is definable, it is already definable by a…

We continue the study of $n$-dependent groups, fields and related structures, largely motivated by the conjecture that every $n$-dependent field is dependent. We provide evidence towards this conjecture by showing that every infinite…

We prove that non-abelian definable, definably simple groups in 1-h-minimal henselian valued fields are essentially already linear algebraic groups. Here, the group is assumed to live in the home sort. We have a similar result in pure…

We formulate a model for the average behaviour of ray class groups of real quadratic fields with respect to a fixed rational modulus, locally at a finite set $S$ of odd primes. To that end, we introduce Arakelov ray class groups of a number…

We characterise the complex interpolation spaces of weighted vector-valued Sobolev spaces with and without boundary conditions on the half-space and on smooth bounded domains. The weights we consider are power weights that measure the…

We give here a semi-analytic formula for the density of critical values for chi random fields on a general manifold. The result uses Kac-Rice argument and a convenient representation for the Hessian matrix of chi fields, which makes the…

We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality…

For some physics students, the concept of a particle travelling faster than the speed of light holds endless fascination, and Cherenkov radiation is a visible consequence of a charged particle travelling through a medium at locally…

For field theories in curved spacetime, defining how matter gravitates is part of the theory building process. In this letter, we adopt Bekenstein's multiple geometries approach to allow part of the matter sector to follow the geodesics on…

Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting…

We study the algebraic implications of the non-independence property (NIP) and variants thereof (dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a…

In this paper, we establish the weighted anisotropic Hardy and Rellich type inequalities with boundary terms for general (real-valued) vector fields. As consequences, we derive new as well as many of the fundamental Hardy and Rellich type…

We show a conditional exactness statement for the Nisnevich Gersten complex associated to an $\mathbb{A}^1$-invariant cohomology theory with Nisnevich descent for smooth schemes over a Dedekind ring with only infinite residue fields. As an…