Related papers: Ray Class Groups of Quadratic and Cyclotomic Field…

In this paper, we will calculate the number of Galois extensions of local fields with Galois group A_n and S_n.

The Polya group of a number field K is the subgroup of the class group of K generated by the classes of the products of the maximal ideals with same norm. A Polya field is a number field whose Polya group is trivial. Our purpose is to start…

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

Let $k$ be an algebraically closed field of characteristic zero, $F$ be an algebraically closed extension of $k$ of transcendence degree one, and $G$ be the group of automorphisms over $k$ of the field $F$. The purpose of this note is to…

It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields…

We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlying number field. This does not solve the open question…

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 -…

This paper is on the inverse parameterized differential Galois problem. We show that surprisingly many groups do not occur as parameterized differential Galois groups over K(x) even when K is algebraically closed. We then combine the method…

Let p be a prime number and M a quadratic number field, M not equal to Q(\sqrt{p}) if p is congruent to 1 modulo 4. We will prove that for any positive integer d there exists a Galois extension F/Q with Galois group D_{2p} and an elliptic…

We study the ramification groups of finite Galois extensions $L/K$ of a complete discrete valuation field $K$ of equal characteristic $p>0$ with perfect residue field and Galois group isomorphic to the group of unitriangular matrices…

Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we investigate the explicit Galois structure of the…

We compute the Galois group of the maximal 2-ramified pro-2-extension of a 2-rational number field

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…

One of the fundamental questions in current field theory, related to Grothendieck's conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the…

Explicit bounds are given on the norms of prime ideals generating arbitrary subgroups of ray class groups of number fields, assuming the Extended Riemann Hypothesis. These are the first explicit bounds for this problem, and are…

In this paper we are interested in the class numbers of a family of real quadratic fields for which the square roots of the discriminants have a known expansion in continued fraction. In particular we prove that $h(D)>1$, with possibly a…

We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.

This paper characterizes the cyclicity property of $2$-power cyclotomic extensions through various means: the structure of the Galois groups, the nature of their subextensions, tower decompositions, and, most importantly, specific…

If k is a commutative field and G a reductive (connected) algebraic group over k, we give bounds for the orders of the finite subgroups of G(k); these bounds depends on the type of G and on the Galois groups of the cyclotomic extensions of…

Let n be an odd number and F an imaginary quadratic field with odd discriminant. We show that there exists infinitely many cubic fields K such that the class number of K is divisible by n and the Galois closure of K contains F.