Related papers: On Field Generated by Division Points of Several F…
The article investigates several questions about field generated by certain formal group laws. This is continuation of a study initiated by the author in prior article titled 'Field Generated by Division Points of Certain Formal Group…
In this article we study the Galois group of field generated by division points of special class of formal group laws and prove an equivalent condition for the group to be abelian. Further, we explore relations between the endomorphism ring…
Several questions about the Galois group of field generated by certain one dimensional formal group laws are studied. This is continuation of author's prior article titled 'Field Generated by Division Points of Certain Formal Group Laws -…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
We give an asymptotic lower bound on the number of field extensions generated by algebraic points on superelliptic curves over $\mathbb{Q}$ with fixed degree $n$ and discriminant bounded by $X$. For $C$ a fixed such curve given by an affine…
In previous work, the authors confirmed the speculation of J. G. Thompson that certain multiquadratic fields are generated by specified character values of sufficiently large alternating groups $A_n$. Here we address the natural…
Let $k$ be a number field, suppose that $B$ is a central simple division algebra over $k$, and choose any maximal order $\mathcal{D}$ of $B$. The object of this paper is to show that the group $\mathcal{D}_S^*$ of $S$-units of $B$ is…
We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the structure of their automorphism groups is clarified and the…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
In this paper, we construct a class of $2$-dimensional formal groups over $\mathbb{Z}_p$ that provide a higher-dimensional analogue of the usual $1$-dimensional Lubin-Tate formal groups, then we initiate the study of the extensions…
Let $E$ be an elliptic curve without complex multiplication defined over a number field $K$ which has at least one real embedding. The field $F$ generated by all torsion points of $E$ over $K$ is an infinite, non-abelian Galois extension of…
The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.
We show that the semi-simplicity conjecture for finitely generated fields follows from the conjunction of the semi-simplicity conjecture for finite fields and for the maximal abelian extension of the field of rational numbers.
We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety $G$ defined over a finite field with a closed subvariety $X\subset G$.
Let $X$ be a projective variety over a number field $K$ endowed with a height function associated to an ample line bundle on $X$. Given an algebraic extension $F$ of $K$ with a sufficiently big Northcott number, we can show that there are…
This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…
We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be…
This paper establishes a relationship between finite extensions and norm groups of formally real quasilocal fields, which yields a generally nonabelian local class field theory, including analogues to the fundamental correspondence, the…
We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.