Related papers: A note on the effective listing of complete types

In view of applications to conformal field theory or to other branches of theoretical physics and mathematics, new examples of character tables for Drinfeld doubles of finite groups (modular data) are made available on a website.

There are abundant results on Diophantine approximation over fields of positive characteristic (see the survey papers [13, 25]), but there is very little information about simultaneous approximation. In this paper, we develop a technique of…

We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.

In the model of synthetic differential geometry consisting of sheaves (with respect to open covers) over the opposite category of the category of closed finitely generated C-infinity rings, any morphism from S, the zeroes of the "amazing…

Let $K$ be a field of characteristic zero. We deal with the algebraic closure of the field of fractions of the ring of formal power series $K[[x_1,\ldots,x_r]]$, $r\geq 2$. More precisely, we view the latter as a subfield of an iterated…

Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and…

In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…

We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any…

The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of…

We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are…

The purpose of this survey is to explain some recent results about analogies between characteristic 0 and characteristic $p>0$ geometry, and to discuss an infinitesimal variant of motivic cohomology. More specifically, we review results…

Following Hasse's example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these…

The aim of this paper is to characterize continuous endomorphisms in the space of entire functions of exponential type of order $p>0$. Let $A_p$ denote the space of entire functions of $n$ complex variables $z\in{\mathbb C}^n$ of order $p$…

We present an application of elimination theory to the study of singularities over arbitrary fields, particularly to the open problem of resolution. A partial extension of a function, defining resolution of singularities over fields of…

Effective field theories offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. These techniques, developed in particle physics, were…

We give a new syntax independent definition of the notion of a generalized algebraic theory as an initial object in a category of categories with families (cwfs) with extra structure. To this end we define inductively how to build a valid…

We compare modular forms of characteristic $p>0$ (i.e. Drinfeld's modular forms) and automorphic forms. We prove that spaces of these modular forms (which are of characteristic $p$) can be described by function spaces of characteristic…

We classify all finite groups of essential dimension 2 over an algebraically closed field of characteristic 0.

We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that…