Related papers: Arithmetic actions on cyclotomic function fields

In the frame of Mahler's method for algebraic independence we show that the algebraic relations over Q linking the values of functions solutions of a system of functional equations come from the algebraic relations between the functions…

For a subgroup of $PGL(2,q)$ we show how some irreducible polynomials over $\mathbb{F}_q$ arise from the field of invariant rational functions. The proofs rely on two actions of $PGL(2,F)$, one on the projective line over a field $F$ and…

We discuss an action of the Grothendieck-Teichm\"{u}ller proalgebraic group on the linear span of proalgebraic tangles, oriented tangles completed by a filtration of Vassiliev. The action yields a motivic structure on tangles. We derive…

We show that any Lambda-ring, in the sense of Riemann-Roch theory, which is finite etale over the rational numbers and has an integral model as a Lambda-ring is contained in a product of cyclotomic fields. In fact, we show that the category…

We describe Mui invariants in terms of Milnor operations and give a simple proof for Mui's theorem on rings of invariants of polynomial tensor exterior algebras with respect to the action of finite general linear groups. Moreover, we…

We develop a Galois theory for systems of linear difference equations with an action of an endomorphism {\sigma}. This provides a technique to test whether solutions of such systems satisfy {\sigma}-polynomial equations and, if yes, then…

We prove that function fields of varieties of dimension at least two over an algebraic closure of a finite field are determined, modulo purely inseparable extensions, by the quotient by the second term in the lower central series of their…

This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…

It is well known that the Galois group of an extension puts constraints on the structure of the relative ideal class groups. Using only basic parts of the theory of group representations, we give a unified approach to such results.

``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…

We introduce a notion of "Galois closure" for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an S_n degree n extension of fields. Moreover, we prove a number of properties of this…

We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…

We study the homogeneous artinian ideals of the polynomial ring $K[x,y,z]$, generated by the homogenous polynomials of degree $d$ which are invariant under an action of the cyclic group $\mathbb Z/d\mathbb Z$, for any $d\geq 3$. We prove…

We study linear ordinary differential equations which are analytically parametrized on Hermitian symmetric spaces and invariant under the action of symplectic groups. They are generalizations of the classical Lam\'e equation. Our main…

We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and…

We develop a new form of patching that is both far-reaching and more elementary than the previous versions that have been used in inverse Galois theory for function fields of curves. A key point of our approach is to work with fields and…

Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…

In this paper we introduce the notion of a partial action of a groupoid on a ring as well as we give a criteria for the existence of a globalization of it. We construct a Morita context associated to a globalizable partial groupoid action…

A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…

If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$…