相关论文: Arboreal Galois representations and uniformization…

We investigate criteria for algebra extensions that are of Galois type with respect to the coaction of a Hopf algebra or, more generally, a one-sided quotient of a Hopf algebra, or with respect to an entwining. We study the module- and…

The goal of this article is to give an explicit classification of the possible $p$-adic Galois representations that are attached to elliptic curves $E$ with CM defined over $\mathbb{Q}(j(E))$. More precisely, let $K$ be an imaginary…

We propose in this paper an approach to Breuil's conjecture on a Langlands correspondence between $p$-adic Galois representations and representations of $p$-adic Lie groups in $p$-adic topological vector spaces. We suggest that Berthelot's…

In 1992, Avner Ash and Mark McConnell presented computational evidence of a connection between three-dimensional Galois representations and certain arithmetic cohomology classes. For some examples they were unable to determine the attached…

Let $\ell$ be a prime number and let $F$ be a number field and $E/F$ a non-CM elliptic curve with a point $\alpha \in E(F)$ of infinite order. Attached to the pair $(E,\alpha)$ is the $\ell$-adic arboreal Galois representation…

We construct and study universal spaces for birational invariants of algebraic varieties over algebraic closures of finite fields.

We discuss the following two problems: 1) The properties of the multiple zeta-values and their generalizations, multiple polylogarithms at N-th roots of unity; 2) The action of the absolute Galois group on the pro-l-completion of the…

I show that the cohomology of the generic points of algebraic complex varieties becomes {\sl stable} birational invariant, when considered `modulo the cohomology of the generic points of the affine spaces'.

This thesis develops some of the basic model theory of covers of algebraic curves. In particular, an equivalence between the good model-theoretic behaviour of the modular j-function, and the openness of certain Galois representations in the…

We study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the classical gauge groupoid of a principal bundle. When the base algebra is in the centre of the total space algebra, the gauge group…

The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction of an explicit basis of the space of…

We introduce an $\ell$-adic analogue of Gauss's hypergeometric function arising from the Galois action on the fundamental torsor of the projective line minus three points. Its definition is motivated by a relation between the KZ-equation…

The main result of this paper is a characterization of the abelian varieties $B/K$ defined over Galois number fields with the property that the zeta function $L(B/K;s)$ is equivalent to the product of zeta functions of non-CM newforms for…

We study the Galois actions on the l-adic schematic and Artin-Mazur homotopy groups of algebraic varieties. For proper varieties of good reduction over a local field K, we show that the l-adic schematic homotopy groups are mixed…

In this short survey we present the appearance of some combinatorial notions in quantum field theory. We first focus on topological graph polynomials (the Tutte polynomial and its multivariate version) and their relation with the parametric…

Let $K$ be a function field of characteristic $p\geq0$ or a number field over which the $abc$ conjecture holds, and let $\phi(x)=x^d+c \in K[x]$ be a unicritical polynomial of degree $d\geq2$ with $d \not\equiv 0,1\pmod{p}$. We completely…

The Galois representation associated to a p-divisible group over a complete noetherian normal local ring with perfect residue field is described in terms of its Dieudonn\'e display. As a corollary we deduce in arbitrary characteristic…

We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations…

Given an abelian algebraic group $A$ over a global field $F$, $\alpha \in A(F)$, and a prime $\ell$, the set of all preimages of $\alpha$ under some iterate of $[\ell]$ generates an extension of $F$ that contains all $\ell$-power torsion…

We give a new proof of a result due to Breuil and Emerton which relates the splitting behavior at p of the p-adic Galois representation attached to a p-ordinary modular form to the existence of an overconvergent p-adic companion form for f.