Related papers: Artin L-functions to almost monomial Galois groups

Let $K$ be a field, and let $f\in K(z)$ be a rational function of degree $d\geq 2$. The Galois group of the field extension generated by the preimages of $x_0\in K$ under all iterates of $f$ naturally embeds in the automorphism group of an…

We are studing Galois actions on fundamental groups. Using towers of coverings we construct measures on the products of finite copies of Z_p. Using these measures we can calculate coefficients of Galois representations. In the simplest case…

This paper realizes of two families of combinatorial symmetric functions via the complex character theory of the finite general linear group $\mathrm{GL}_{n}(\mathbb{F}_{q})$: chromatic quasisymmetric functions and vertical strip LLT…

In a series of papers, van Geemen and Top have defined a family of surfaces $S_z$ indexed by a nonzero integer parameter $z$, and a compatible family of 3-dimensional Galois representations over $\Q(i)$ attached to each surface. In this…

It is known that a finite group G can only act freely on affine n-space if K has positive characteristic p and G is a p-group. In that case the group action is "non-linear" and the ring of regular functions must be a trace-surjective…

Let $X$ be a smooth, separated, geometrically connected scheme defined over a number field $K$ and $\{\rho_\lambda\}_\lambda$ a system of n-dimensional semisimple $\lambda$-adic representations of the \'etale fundamental group of $X$ such…

We construct new families of quasimorphisms on many groups acting on CAT(0) cube complexes. These quasimorphisms have a uniformly bounded defect of 12, and they "see" all elements that act hyperbolically on the cube complex. We deduce that…

We show that if $K$ is an arbitrary field and $G$ is a finite group then there exists a curve over $K$ with automorphism group $G$. We also give a positive solution to the weak inverse Galois problem for function fields over an arbitrary…

In this paper, we consider Galois representations of the absolute Galois group $\text{Gal}(\overline {\mathbb Q}/\mathbb Q)$ attached to modular forms for noncongruence subgroups of $\text{SL}_2(\mathbb Z)$. When the underlying modular…

We study the Galois groups of polynomials arising from a compatible family of representations with big orthogonal monodromy. We show that the Galois groups are usually as large as possible given the constraints imposed on them by a…

We develop a unified representation theory for the categories of finite subsets and relation-preserving maps of highly homogeneous relational structures classified by Cameron. For any commutative coefficient ring $k$, we extend the…

When k is an algebraically closed field of characteristic 0 and H is a non-semisimple monomial Hopf algebra, we show that all Galois objects over H are determined up to H-comodule algebra isomorphism by their polynomial H-identities,…

We find a polynomial (n^6) isoperimetric function for Artin groups, the defining graph of which contains no edges labelled by 3. This in particular shows that even Artin groups have solvable word problem. We use small cancellation theory of…

We lift the Euler characteristic of a nearly perfect complex to a relative algebraic K-group by passing to its l-adic Euler characteristics.

We give a complete list of rational functions $A$ such that the genus $g$ of the Galois closure of $\mathbb C(z)/\mathbb C(A)$ equals zero. We also provide a geometric description of $A$ for which $g=1.$

Given a pair of n-dimensional complex Galois representations over Q, we define their matching density to be the density, if it exists, of the set of places at which the traces of Frobenius of the two Galois representations are equal. We…

Consider the action of a subgroup $G$ of the permutation group on the polynomial ring $S := k[x_{1}, \ldots, x_{n}]$ via permutations. We show that if $k$ does not have characteristic two, then the following are independent of $k$: the…

According to Liouville's Theorem, an indefinite integral of an elementary function is usually not an elementary function. In this notes, we discuss that statement and a proof of this result. The differential Galois group of the extension…

In the present paper, we give a q-analogue of the Grothendieck conjecture on p-curvatures for q-difference equations defined over the field of rational function K(x), where K is a finite extension of a field of rational functions k(q), with…

Let K be a local field whose residue field is a finite field of characteristic p, and let L/K be a finite totally ramified Galois extension. Fried and Heiermann defined the "indices of inseparability" of L/K, a refinement of the…