Related papers: Chasing maximal pro-p Galois groups via 1-cyclotom…

We prove a criterion for the mildness of a finitely presented pro-$p$ group $G$. It implies as a special case a cohomological mildness criterion via Massey products, generalizing results due to Schmidt and G\"artner. It subsumes Labute's…

Let p be an odd prime. Let K = \Q(zeta) be the p-cyclotomic number field. Let v be a primitive root mod p and sigma : zeta --> zeta^v be a \Q-isomorphism of the extension K/\Q generating the Galois group G of K/\Q. For n in Z, the notation…

We call a pro-$p$ group $G$ Frattini-injective if distinct finitely generated subgroups of $G$ have distinct Frattinis. This paper is an initial effort toward a systematic study of Frattini-injective pro-$p$ groups (and several other…

We determine all the $p$-adic analytic groups that are realizable as Galois groups of the maximal pro-$p$ extensions of number fields with prescribed ramification and splitting under an assumption which allows us to move away from the Tame…

Let $p$ be an irregular prime. Let $K=\Q(\zeta)$ be the $p$-cyclotomic field. From Kummer and class field theory, there exist Galois extensions $S/\Q$ of degree $p(p-1)$ such that $S/K$ is a cyclic unramified extension of degree $[S:K]=p$.…

A Bloch-Kato pro-p group G is a pro-p group with the property that the F_p-cohomology ring of every closed subgroup of G is quadratic. It is shown that either such a pro-p group G contains no closed free pro-p groups of infinite rank, or…

For a number field $K$, we consider $K^{\rm ta}$ the maximal tamely ramified algebraic extension of~$K$, and its Galois group $G^{\rm ta}_K= Gal(K^{ta}/K)$. Choose a prime $p$ such that $\mu_p \not \subset K$. Our guiding aim is to…

Let $p$ be an odd prime and $F$ be a number field whose $p$-class group is cyclic. Let $F_{\{\mathfrak{q}\}}$ be the maximal pro-$p$ extension of $F$ which is unramified outside a single non-$p$-adic prime ideal $\mathfrak{q}$ of $F$. In…

Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H^1(G,…

Let $p$ be a prime. The right-angled Artin pro-$p$ group $G_{\Gamma}$ associated to a fnite simplicial graph $\Gamma$ is the pro-$p$ completion of the right-angled Artin group associated to $\Gamma$. We prove that the following assertions…

We prove that a finitely generated pro-$p$ group acting on a pro-$p$ tree $T$ with procyclic edge stabilizers is the fundamental pro-$p$ group of a finite graph of pro-$p$ groups with edge and vertex groups being stabilizers of certain…

We consider the canonical representation of the absolute Galois group of the rational numbers in the outer automorphism group of the pro-p completion of the fundamental group of the projective line minus 0,1, and infinity. Deligne has…

In this article we survey and examine the realizability of $p$-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of…

In this paper, we utilize our previous results on mod p monodromy of cyclic coverings of the projective line to realize a large series of groups of the form PSL(n, q) and PSU(n, q) as Galois groups over Q. We achieve for the first time a…

For any finite cyclic $p$-group $G$, we will show that every $\mathbb{Z}_p$-torsion free finitely generated $\mathbb{Z}_p[G]$-module appears as $\mathcal{O}_K^\times\otimes_{\mathbb{Z}}\mathbb{Z}_p$ up to $\mathbb{Z}_p[G]$-free direct…

We begin a study of a pro-$p$ analogue of limit groups via extensions of centralizers and call $\mathcal{L}$ this new class of pro-$p$ groups. We show that the pro-$p$ groups of $\mathcal{L}$ have finite cohomological dimension, type…

The absolute Galois group of the cyclotomic field $K={\mathbb Q}(\zeta_p)$ acts on the \'etale homology of the Fermat curve $X$ of exponent $p$. We study a Galois cohomology group which is valuable for measuring an obstruction for…

Let $p$ be a prime number, $F$ a field containing a root of unity of order $p$, and $G_F$ the absolute Galois group. Extending results of Hopkins, Wickelgren, Minac and Tan, we prove that the triple Massey product $H^1(G_F)^3\to H^2(G_F)$…

Let $F$ be a number field, abelian over the rational field, and fix a odd prime number $p$. Consider the cyclotomic $Z_p$-extension $F_\infty/F$ and denote $F_n$ the ${n}^{\rm th}$ finite subfield and $C_n$ its group of circular units. Then…

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…