Related papers: On Field Generated by Division Points of Several F…
We introduce a ring and a field, generated by a semigroup, and we investigate some of their properties.
Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a…
Degree bounds for algebra generators of invariant rings are a topic of longstanding interest in invariant theory. We study the analogous question for field generators for the field of rational invariants of a representation of a finite…
This second part of the paper strengthens the descent theory described in the first part to rational maps, arbitrary base fields, and dynamics given by correspondences. We obtain in particular a decomposition of any difference field…
In this paper we construct number fields ramified at 2 and 3 only, with various moderate-sized non-solvable Galois groups. We construct these fields by specializing three point covers, some from the literature and some new here. The…
This paper is the sequel of our paper "Arithmetic height functions over finitely generated fields" (cf. math.NT/9809016). In this paper, we define the canonical height of subvarieties of an abelian variety over a finitely generated field…
Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.
We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous results of M. Fried and Takahashi on the global field case.
We show that any Kahler extension of a finitely generated abelian group by a surface group of genus g at least 2 is virtually a product. Conversely, we prove that any homomorphism of an even rank, finitely generated abelian group into the…
We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
Let $L$ and $M$ be two algebraically closed fields contained in some common larger field. It is obvious that the intersection $C=L\cap M$ is also algebraically closed. Although the compositum $LM$ is obviously perfect, there is no reason…
Finite collections of point masses contained in some bounded domain produce a unique field in the exterior domain, which means that the associated basis functions (often called ``fundamental solutions'') are independent. A new proof of this…
This paper is mainly motivated by the analysis of the so-called Bounded Generation property (BG) of linear groups (in characteristic $0$), which is known to admit far-reaching group-theoretic implications. We achieve complete answers to…
We give an explicit necessary condition for pairs of orders in a quartic CM-field to have the same polarised class group. This generalises a simpler result for imaginary quadratic fields. We give an application of our results to computing…
Some results that are true in classical groups are investigated in generalized groups and are shown to be either generally true in generalized groups or true in some special types of generalized groups. Also, it is shown that a Bol groupoid…
It has often been observed that the Multifractal Formalism and the Large Deviation Principles are intimately related. In fact, Multifractal Formalism was heuristically derived using the Large Deviations ideas. In numerous examples in which…
This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the…
Roth's theorem is extended to finitely generated field extensions of $\Bbb Q$, using Moriwaki's framework for heights.
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…
The P\'{o}lya group of an algebraic number field is the subgroup generated by the ideal classes of the products of prime ideals of equal norm inside the ideal class group. Inspired by a recent work on consecutive quadratic fields with large…