Related papers: Tree representations of Galois groups

Inspired by Ol'shanskii's work, we provide an axiomatic framework to describe certain irreducible unitary representations of non-discrete unimodular totally disconnected locally compact groups. We then look at the applications to certain…

Let $N/K$ be a finite Galois extension of $p$-adic number fields and let $\rho^\mathrm{nr} : G_K \to \mathrm{Gl}_r(\mathbb Z_p)$ be an $r$-dimensional unramified representation of the absolute Galois group $G_K$ which is the restriction of…

The Elementary Type Conjecture in Galois theory provides a concrete inductive description of the finitely generated maximal pro-$p$ Galois groups $G_F(p)$ of fields $F$ containing a root of unity of order $p$. We describe several variants…

We prove the modularity of minimally ramified ordinary residually reducible p-adic Galois representations of an imaginary quadratic field F under certain assumptions. We first exhibit conditions under which the residual representation is…

We study deformation theory of mod $p$ Galois representations of $p$-adic fields with values in generalised reductive group schemes, such as $L$-groups and $C$-groups. We show that the corresponding deformation rings are complete…

For any simple algebraic group $G$ of exceptional type, we construct geometric $\ell$-adic Galois representations with algebraic monodromy group equal to $G$, in particular producing the first such examples in types $\mathrm{F}_4$ and…

We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group's action on the division points of an…

Let $F$ be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations $Gal(\bar{F}/F) \to PGL_n(C)$ lift to $GL_n(C)$. We take…

Crystabelline representations are representations of the absolute Galois group $G_{\mathbb{Q}_p}$ over $\mathbb{Q}_p$ that become crystalline on $G_{F}$ for some abelian extension $F/\mathbb{Q}_p$. Their relation to modular forms is that…

We study the arithmetic and geometric iterated monodromy groups associated to the postcritically finite (PCF) quadratic rational function $f(x)=\frac{2}{(x-1)^2}$ defined over a number field $k$, whose critical points are both strictly…

For every finite group $H$ and every finite $H$-module $A$, we determine the subgroup of negligible classes in $H^2(H,A)$, in the sense of Serre, over fields with enough roots of unity. As a consequence, we show that for every odd prime…

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…

We study isometric actions of tree automorphism groups on the infinite-dimensional hyperbolic spaces. On the one hand, we exhibit a general one-parameter family of such representations and analyse the corresponding equivariant embeddings of…

Let A be a basic connected finite dimensional algebra over an algebraically closed field, let G be a group, let T be a basic tilting A-module and let B the endomorphism algebra of T. Under a hypothesis on T, we establish a correspondence…

We give a direct approach to recover some of the results of Wiles and Tayor on modularity of certain 2-dimensional p-adic representations of the absolute Galois group of Q.

In this paper we study the images of certain families $\{\rho_{\pi,\ell} \}_\ell$ of $G_2$-valued Galois representations of $\mbox{Gal}(\overline{F}/F)$ associated to $L$-algebraic regular, self-dual, cuspidal automorphic representations…

We construct an infinite family of representations of finite groups with an irreducible adjoint action and we give an application to the question of lacunary of Frobenius traces in Galois representations.

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…

The action of the absolute Galois group $\text{Gal}(K^{\text{ksep}}/K)$ of a global field $K$ on a tree $T(\phi, \alpha)$ of iterated preimages of $\alpha \in \mathbb{P}^1(K)$ under $\phi \in K(x)$ with $\text{deg}(\phi) \geq 2$ induces a…

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…