Related papers: Two-Dimensional Local-Global Class Field Theory in…

We construct a framework which unifyies in dual pairs the fields and anti-fields of the Batalin and Vilkovisky quantization method. We consider gauge theories of p-forms coupled to Yang-Mills fields. Our algorithm generates many topological…

We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…

Let $\breve{K}$ be a complete discrete valuation field with an algebraically closed residue field ${k}$ and ring of integers $\breve{{O}}$. Let $T$ be a torus defined over $\breve{K}$. Let $L^+T$ denote the connected commutative…

Viewing higher local fields as ring objects in the category of iterated pro-ind-objects, a definition of open subgroups in Milnor K-groups of the fields is given. The self-duality of the additive group of a higher local field is proved. By…

One can associate to a valued field an inverse system of valued hyperfields $(\mathcal{H}_i)_{i \in I}$ in a natural way. We investigate when, conversely, such a system arise from a valued field. First, we extend a result of Krasner by…

In this expository paper we provide a geometric proof of the local Langlands Correspondence for the groups $\operatorname{GL}_{1}$ defined over $p$-adic fields $K$. We do this by redeveloping the theory of proalgebraic groups and use this…

In the language of $L^\infty$-modules proposed by Gigli, we introduce a first order calculus on a topological Lusin measure space $(M,\mathfrak{m})$ carrying a quasi-regular, strongly local Dirichlet form $\mathscr{E}$. Furthermore, we…

We describe a topological field theory that studies the moduli space of solutions of the symplectic vortex equations. It contains as special cases the topological sigma-model and topological Yang-Mills over Kahler surfaces. The correlation…

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…

We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive…

We extend the characterization of extremal valued fields given in \cite{[AKP]} to the missing case of valued fields of mixed characteristic with perfect residue field. This leads to a complete characterization of the tame valued fields that…

Smooth irreducible representations of tori over local fields have been parameterized by Langlands, using class field theory and Galois cohomology. This paper extends this parameterization to central extensions of such tori, which arise…

In this paper we study some special classes of division algebras over a Laurent series field with arbitrary residue field. We call the algebras from these classes as splittable and good splittable division algebras. It is shown that these…

Two fields are Witt equivalent if their Witt rings of symmetric bilinear forms are isomorphic. Witt equivalent fields can be understood to be fields having the same quadratic form theory. The behavior of finite fields, local fields, global…

We present an intimate connection among the following fields: (a) distributed local algorithms: coming from the area of computer science, (b) finitary factors of iid processes: coming from the area of analysis of randomized processes, (c)…

We show that every smooth projective curve over a finite field k admits a finite tame morphism to the projective line over k. Furthermore, we construct a curve with no such map when k is an infinite perfect field of characteristic two. Our…

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…

We prove a theorem of Tits type for automorphism groups of projective varieties over an algebraically closed field of arbitrary characteristic, which was first conjectured by Keum, Oguiso and Zhang for complex projective varieties.

Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…

Let $q$ be a unimodular quadratic form over a field $K$. Pfister's famous local--global principle asserts that $q$ represents a torsion class in the Witt group of $K$ if and only if it has signature $0$, and that in this case, the order of…