相关论文: Towers of function fields with extremal properties

To connect arithmetic and ring-theoretic properties of rings of mixed characteristic with those of positive characteristic, we introduce monoidal maps for perfectoid towers. Using these maps, we discuss the almost integrality of perfectoid…

Experimental results on hadronic structures are discussed in view of our physics understanding. Achievements and challenges are noted.

We construct a tower of fields from the rings $R_n$ which parametrize pairs $(X,\lambda)$, where $X$ is a deformation of a fixed one-dimensional formal group $\mathbb{X}$ of finite height $h$, together with a Drinfeld level-$n$ structure…

The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…

The phase structure of the scalar field theory with arbitrary powers of the gradient operator and a local non-analytic potential is investigated by the help of the RG in Euclidean space. The RG equation for the generating function of the…

Non equilibrium effective field theory is presented as an inhomogeneous field theory, using a formulation which is analogous to that of a gauge theory. This formulation underlines the importance of structural aspects of non-equilibrium,…

An extremal property of finite Schur sigma-groups G is described in terms of their path to the root in the descendant tree of their abelianization G/G'. The phenomenon is illustrated and verified by all known examples of Galois groups…

Imposing Huygens' Principle in a 4D Wightman QFT puts strong constraints on its algebraic and analytic structure. These are best understood in terms of ``biharmonic fields'', whose properties reflect the presence of infinitely many…

Positive configurations of points in the affine building were introduced in \cite{Le} as the basic object needed to define higher laminations. We start by giving a self-contained, elementary definition of positive configurations of points…

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…

We briefly review the structure and properties of self-dual field actions.

This document describes the authors' current research project: the evaluation of a tower of Rankin-Selberg integrals on the group E_6. We recall the notion of a tower, and two known towers, making observations about how the integrals within…

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…

We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…

We show that in general for a given group the structure of a maximal hyperbolic tower over a free group is not canonical: We construct examples of groups having hyperbolic tower structures over free subgroups which have arbitrarily large…

Metrical completeness for Bruhat-Tits buildings is a natural and useful condition. In this paper we determine which Bruhat-Tits buildings are metrically complete up to certain cases involving infinite-dimensionality and residue…

We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field. We deduce lower bounds and…

The first examples of exceptional terminal singularities are constructed.

We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…