Related papers: Maximal $2$-extensions of Pythagorean fields and R…

We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous paper by three of the authors. We first…

We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous paper by three of the authors. We first…

A major open problem in current Galois theory is to characterize those profinite groups which appear as absolute Galois groups of various fields. Obtaining detailed knowledge of the structure of quotients and subgroup filtrations of Galois…

We compute the Galois group of the maximal 2-ramified and complexified pro-2-extension of any 2-rational number field.

For an integer $m\geq 2$, we aim to investigate the realizability of types of metacyclic-nonmodular groups, whose abelianization is $\mathbb{Z}/2 \mathbb{Z}\times\mathbb{Z}/2^m \mathbb{Z}$, as the Galois group of the maximal unramified…

We investigate the Galois cohomology of finitely generated maximal pro-$p$ quotients of absolute Galois groups. Assuming the well-known conjectural description of these groups, we show that Galois cohomology has the PBW property. Hence in…

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…

Using the mixed Lie algebras of Lazard, we extend the results of the first author on mild groups to the case p=2. In particular, we show that for any finite set S_0 of odd rational primes we can find a finite set S of odd rational primes…

We prove that certain fields have the property that their absolute Galois groups are free as profinite groups: the function field of a real curve with no real points; the maximal abelian extension of a 2-variable Laurent series field over a…

We prove that a strengthened version of Minac-Tan's Massey Vanishing Conjecture holds true for fields with a finite number of square classes whose maximal pro-$2$ Galois group is of elementary type (as defined by I. Efrat). In particular,…

Let F be a finite field. We prove that the cohomology algebra with coefficients in F of a right-angled Artin group is a strongly Koszul algebra for every finite graph ${\Gamma}$. Moreover, the same algebra is a universally Koszul algebra…

Let $G$ be a subgroup of ${\rm PGL}_2({\mathbb F}_q)$, where $q$ is any prime power, and let $Q \in {\mathbb F}_q[x]$ such that ${\mathbb F}_q(x)/{\mathbb F}_q(Q(x))$ is a Galois extension with group $G$. By explicitly computing the Artin…

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

We construct two families of examples of pro-p groups, with rather elementary presentations, that do not complete into 1-cyclotomic oriented pro-p groups. These provide brand new examples of pro-p groups that do not occur as maximal pro-p…

We give several equivalent characterisations of the maximal pro-2 quotients of real projective groups. In particular, for pro-2 real projective groups we provide a presentation in terms of generators and relations, and a purely…

We consider the Galois group $G_2(K)$ of the maximal unramified $2$-extension of $K$ where $K/\mathbb{Q}$ is cyclic of degree $3$. We also consider the group $G^+_2(K)$ where ramification is allowed at infinity. In the spirit of the…

Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam-Liu-Sharifi-Wake-Wang. We prove that the pro-p completion of the right-angled Artin group associated to a chordal simplicial graph is of p-absolute Galois…

- Let K be a totally imaginary number field. Denote by G ur K (2) the Galois group of the maximal unramified pro-2 extension of K. By comparing cup-products in {\'e}tale cohomology of SpecO K and cohomology of uniform pro-2 groups, we…

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…

We introduce a criterion on the presentation of finitely presented pro-$p$ groups which allows us to compute their cohomology groups and infer quotients of mild groups of cohomological dimension strictly larger than two, from (non-free)…