Related papers: The Galois Action on Consistent Maps

Let $F$ be a local field of characteristic $p>0$. By adapting methods of Scholze, we give a new proof of the local Langlands correspondence for $\GL_n$ over $F$. More specifically, we construct $\ell$-adic Galois representations associated…

A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are carefully chosen, they provide compatible…

We study the locus of fixed points of a torus action on a GIT quotient of a complex vector space by a reductive complex algebraic group which acts linearly. We show that, under the assumption that $G$ acts freely on the stable locus, the…

Let $G$ be a locally compact group. For every $G$-flow $X$, one can consider the stabilizer map $x \mapsto G_x$, from $X$ to the space $\mathrm{Sub}(G)$ of closed subgroups of $G$. This map is not continuous in general. We prove that if one…

The moduli space of stable pairs on a local surface $X=K_S$ is in general non-compact. The action of $\mathbb{C}^*$ on the fibres of $X$ induces an action on the moduli space and the stable pair invariants of $X$ are defined by the virtual…

We outline a project to study the Galois action on a class of modular graphs (special type of dessins) which arise as the dual graphs of the sphere triangulations of non-negative curvature, classified by Thurston. Because of their…

A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The…

Let X be a Hausdorff topological group and G a locally compact subgroup of X. We show that the natural action of G on X is proper in the sense of R. Palais. This is applied to prove that there exists a closed set F of X such that FG=X and…

Teichmueller curves are geodesic discs in Teichmueller space that project to algebraic curves $C$ in the moduli space $M_g$. Some Teichm\"uller curves can be considered as components of Hurwitz spaces. We show that the absolute Galois group…

Consider a finite group $G$ acting on a Riemann surface $S$, and the associated branched Galois cover $\pi_G:S \to Y=S/G$. We introduce the concept of geometric signature for the action of $G$, and we show that it captures the information…

For a Galois number field $K$, the Galois group $\text{Gal}(K/\mathbb{Q})$ acts on the class group $Cl_K$ in a very natural way: $\sigma\cdot[I]=[\sigma(I)]$ for any $\sigma \in \text{Gal}(K/\mathbb{Q})$, $[I]\in Cl_K$. In this paper, we…

The automorphism group of the Galois covering induced by a pluri-canonical generic covering of a projective space is investigated. It is shown that by means of such coverings one obtains, in dimensions one and two, serieses of specific…

Let $G$ be an infinite discrete group and let $\underline{E}G$ be a classifying space for proper actions of $G$. Every $G$-equivariant vector bundle over $\underline{E}G$ gives rise to a compatible collection of representations of the…

We analize the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a unified way. Then we study their representations…

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of…

On a Weierstrass elliptic surface, we describe the action of the relative Fourier-Mukai transform on the geometric chamber of $\mathrm{Stab}(X)$, and in the K3 case we also study the action on one of its boundary components. Using new…

Let $C$ be a complex algebraic curve uniformised by a Fuchsian group $\Gamma$. In the first part of this paper we identify the automorphism group of the solenoid associated with $\Gamma$ with the Belyaev completion of its commensurator…

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

We prove several superrigidity results for isometric actions on metric spaces satisfying some convexity properties. First, we extend some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of…

We discuss the problem of when a continuous map between topological spaces induces a continuous function between their respective hyperspaces. We characterize the continuity of the induced function in the case of the Fell and Attouch-Wets…