相关论文: Groups interpretable in theories of fields

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…

Let $T$ be a complete theory of fields, possibly with extra structure. Suppose that model-theoretic algebraic closure agrees with field-theoretic algebraic closure, or more generally that model-theoretic algebraic closure has the exchange…

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

We investigate Diophantine definability and decidability over some subrings of algebraic numbers contained in quadratic extensions of totally real algebraic extensions of $\mathbb Q$. Among other results we prove the following. The big…

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

Field Arithmetic studies the interplay between arithmetical properties of fields and their absolute Galois groups. Here we studies fields satisfying local global principles for rational points of varieties and profinite groups satisfying…

We determine the irreducible constituents of the Steinberg character of an orthogonal group over a finite field restricted to the orthogonal group of one less dimension

We settle some open problems in the special case of groups in o-minimal structures, such as the equality of G^00 and G^000 and the equivalence of definable amenability and existence of a type with bounded orbit. We prove almost exactness of…

Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.

The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all…

We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…

We present a geometric framework for discrete classical field theories, where fields are modeled as "morphisms" defined on a discrete grid in the base space, and take values in a Lie groupoid. We describe the basic geometric setup and…

We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and…

These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…

Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued fields. As an application we prove many-one reductions…

We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…