Related papers: Genus fields of global fields

We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret's result about the ideal class group problem. Another is a…

We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field…

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

We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We deduce a classification of any Galois cubic extension of a…

It is shown that any finitely generated subring of a global field has a universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring of integers and its subsequent extensions to rings of integers in…

We give a construction of the genus field for Kummer $\ell^n$-cyclic extensions of rational congruence function fields, where $\ell$ is a prime number. First, we compute the genus field of a field contained in a cyclotomic function field,…

We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established. The proof is classical, employing well-known results from congruence function field theory.

It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different…

In this work we present some arithmetic properties of families of abelian $p$--extensions of global function fields, among which are their generators and their type of ramification and decomposition.

Let $K/k$ be a finite extension of a global field. Such an extension can be generated over $k$ by a single element. The aim of this article is to prove the existence of a "small" generator in the function field case. This answers the…

In this paper, we use counting theorems from the geometry of numbers to extend the Riemann-Roch theorem and the Riemann-Hurwitz formula to global fields of arbitrary characteristic.

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.

In this paper we start a classification of certain global integrals. First, we use the language of unipotent orbits to write down a family of global integrals. We then classify all those integrals which satisfy the dimension equation we…

We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.

We discuss the notions of indices of vector fields and 1-forms and their generalizations to singular varieties and varieties with actions of finite groups, as well as indices of collections of vector fields and 1-forms.

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.