Related papers: Galois groups and cohomological functors

The p-class tower $F_p^\infty(k)$ of a number field k is its maximal unramified pro-p extension. It is considered to be known when the p-tower group, that is the Galois group $G:=Gal(F_p^\infty(k)/k)$, can be identified by an explicit…

For a rational prime $p\neq 2$, we compute the sequence of ramification groups of a Galois, radical and finite extension $L/F$ where $F/\mathbb{Q}_p$ is an unramified finite extension. First, we compute it in the case where the exponent of…

For fields F of characteristic not p containing a primitive $p$th root of unity, we determine the Galois module structure of the group of $p$th-power classes of K for all cyclic extensions K/F of degree p.

Let $K$ be a field with $G_K(2) \simeq G_{\mathbb{Q}}(2)$, where $G_F(2)$ denotes the maximal pro-2 quotient of the absolute Galois group of a field $F$. We prove that then $K$ admits a (non-trivial) valuation $v$ which is 2-henselian and…

Let $F$ be a number field, $f$ an algebraic automorphic newform on $\mathrm{GL}(2)$ over $F$, $p$ an odd prime does not divide the class number of $F$ and the level of $f$. We prove that $f$ is determined by its $L$-values twisted by Galois…

Let p be an odd prime, K a finite extension of Q_p, G=Gal(\bar K/K) the Galois group and e=e(K/Q_p) the ramification index. Suppose T is a p^n torsion representation such that T is isomorphic to a quotient of two G-stable Z_p-lattices in a…

In this paper, we first discuss some properties of the Galois linear maps. We provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups as its applications. Then let $H$ be a Hopf quasigroup with bijective antipode and…

Suppose $\mathcal K$ is $N$-dimensional local field of characteristic $p$, $\mathcal G =\mathop{Gal}(\mathcal K_{sep}/\mathcal K)$, $\mathcal G_{<p}$ is the maximal quotient of $\mathcal G$ of period $p$ and nilpotent class $<p$ and…

We prove the existence of certain rationally rigid triples in F_4(p) for good primes p (i.e., p>3), thereby showing that these groups occur as regular Galois groups over Q(t) and so also over Q. We show that these triples give rise to rigid…

We show that the simple group PSL_2(F_p) occurs as the Galois group of an extension of the rationals for all primes p>3. We obtain our Galois extensions by studying the Galois action on the second etale cohomology groups of a specific…

Let $K$ be a field whose characteristic is prime to a fixed integer $n$ with $\mu_n \subset K$, and choose $\omega \in \mu_n$ a primitive $n$th root of unity. Denote the absolute Galois group of $K$ by $\operatorname{Gal}(K)$, and the…

This paper establishes restrictions on the possible Galois actions on the pro-l-unipotent fundamental group of a smooth variety X of good reduction over a local field K. In particular, if X is proper and l is not equal to the residue…

Given a finite group $\Gamma$, we prove results on the distribution of the prime-to-$q|\Gamma|$ part of fundamental groups of $\Gamma$-covers of the projective line $\mathbb P^1_{\mathbb F_q}$ over a finite field $\mathbb F_q$ as…

Let $X$ be a variety (possibly non-complete or singular) over a finitely generated field $k$ of characteristic $0$. For a prime number $\ell$, let $\rho_\ell$ be the Galois representation on the first $\ell$-adic cohomology of $X$. We show…

We compute the Galois group of the splitting field $F$ of any irreducible and separable polynomial $f(x)=x^6+ax^3+b$ with $a,b\in K$, a field with characteristic different from two. The proofs require to distinguish between two cases:…

Information about the absolute Galois group $G_K$ of a number field $K$ is encoded in how it acts on the \'etale fundamental group $\pi$ of a curve $X$ defined over $K$. In the case that $K=\mathbb{Q}(\zeta_n)$ is the cyclotomic field and…

The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to…

This paper presents results on both the kernel and cokernel of the S-capitulation map C_{F,S}\ra C_{K,S}^{G} for arbitrary finite Galois extensions K/F (with Galois group G) and arbitrary finite sets of primes S of F (assumed to contain the…

Let $ F$ be an imaginary quadratic field and $\mathcal{O}$ its ring of integers. Let $ \mathfrak{n} \subset \mathcal{O} $ be a non-zero ideal and let $ p> 5$ be a rational inert prime in $F$ and coprime with $\mathfrak{n}$. Let $ V$ be an…

Let $k$ be a real abelian number field and $p$ an odd prime not dividing $[k:\mathbb{Q}]$. For a natural number $d$, let $E_d$ denote the group of units of $k$ congruent to $1$ modulo $d$, $C_d$ the subgroup of $d$-circular units of $E_d$,…