Related papers: Galois Groups and Genera of a kind of Quasi-cyclot…

In the present paper, we give a q-analogue of the Grothendieck conjecture on p-curvatures for q-difference equations defined over the field of rational function K(x), where K is a finite extension of a field of rational functions k(q), with…

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…

In this paper, we want to control the geometry of some surface subgroups of a cocompact Kleinian group. More precisely, provided any genus-2 quasi-Fuchsian group $\Gamma$ and cocompact Kleinian group $G$, then for any $K>1$, we will find a…

The K-theory of a functor may be viewed as a relative version of the K-theory of a ring. In the case of a Galois extension of a number field F/L with rings of integers A/B respectively, this K-theory of the "norm functor" is an extension of…

For each finite subgroup $G$ of $PGL_2(\mathbb{Q})$, and for each integer $n$ coprime to $6$, we construct explicitly infinitely many Galois extensions of $\mathbb{Q}$ with group $G$ and whose ideal class group has $n$-rank at least…

We extend the Gelfand and Graev construction of generalized Fourier transforms on basic affine space from split groups to quasi-split groups over a local non-archimedean field $F$.

In this paper, we find all the generic polynomials for geometric $\ell$-cyclic function field extensions over the finite fields $\mathbb{F}_q$ where $q= p^n$, $p$ prime integer such that $q \equiv -1 \mod \ell$ and $(\ell , p)=1$.

We construct and study fields F with the property that F has infinitely many extensions of some fixed degree, but E*/(E*)^n is finite for every finite extension E of F and every n>0.

We say that a group is {\em almost abelian} if every commutator is central and squares to the identity. Now let $G$ be the Galois group of the algebraic closure of the field $\QQ$ of rational numbers in the field of complex numbers. Let…

Let $k\subseteq K$ be a finite Galois extension of fields with Galois group $G$. Let $\mathscr{G}$ be the automorphism $k$-group scheme of $K$. We construct a canonical $k$-subgroup scheme $\underline{G}\subset\mathscr{G}$ with the property…

We construct \'etale generalized Heisenberg group covers of hyperelliptic curves over number fields. We use these to produce infinite families of quadratic extensions of cyclotomic fields that admit everywhere unramified generalized…

A Galois field extension $E/F$ whose Galois group is a pro-2-group of an exponent of at most 8, with a nilpotency class of at most 4, is determined, such that it contains essential information about the Witt rings of all quadratic…

We study certain unitary CM fields whose Galois closure has Galois group $\operatorname{PSL}_2(\mathbb{F}_q) \times \mathbb{Z}/2\mathbb{Z}$. After investigating the CM types of these fields, we turn towards Colmez's conjectural formula on…

Let $f:X\to Y$ be a surjective morphism of integral schemes. Then $X$ is said to be quasi-galois closed over $Y$ by $f$ if $X$ has a unique conjugate over $Y$ in an algebraically closed field. Such a notion has been applied to the…

Let k be a number field and K/k Galois. We transform the construction of the unramified Brauer group of the norm one torus R^1_K/k(G_m) into the construction of a special abelian extension over K. If k=Q and K/Q biquadratic, we explicitly…

In 2020, Alabdali and Byott described the Hopf-Galois structures arising on Galois field extensions of squarefree degree. Extending to squarefree separable, but not necessarily normal, extensions $L/K$ is a natural next step. One must…

Let $p$ be a prime, and $q$ a power of $p$. Using Galois theory, we show that over a field $K$ of characteristic zero, the endomorphism algebras of the jacobians of certain superelliptic curves $y^q=f(x)$ are products of cyclotomic fields.

Complex functions $\chi (m)$ where $m$ belongs to a Galois field $GF(p^ \ell)$, are considered. Fourier transforms, displacements in the $GF(p^ \ell) \times GF(p^ \ell)$ phase space and symplectic $Sp(2,GF(p^ \ell))$ transforms of these…

In this paper we obtain the genus field of a general Kummer extension of a global rational function field. We study first the case of a general Kummer extension of degree a power of a prime. Then we prove that the genus field of a composite…

Let $L/K$ be a finite Galois extension whose Galois group $G$ is non-abelian and characteristically simple. Using tools from graph theory, we shall give a closed formula for the number of Hopf-Galois structures on $L/K$ with associated…