Related papers: Automorphism groups of curves over arbitrary field…

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 prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

For bounded pseudoconvex domains with finite type we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different points of the boundary, then the automorphism group has…

Let K be a field and G a finite group. The question of 'admissibility' of G over K was originally posed by Schacher, who gave partial results in the case K = Q. In this paper, we give necessary conditions for admissibility of a finite group…

The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the…

We give a detailed description of the algebraic group Aut(g) of automorphisms of a simple finite dimensional Lie superalgebra g over an algebraically closed field k of characteristic 0. We also give a description of the group of…

Motivated by the analogy between number fields and function fields, this paper extends the main result of \cite{janbazi2025unified} to the function field setting. Let $C$ be a smooth affine curve over a finite field, and let $\pi: S…

Given a number field $F$, a finite group $G$ and an indeterminate $T$, {\it{a $G$-parametric extension over $F$}} is a finite Galois extension $E/F(T)$ with Galois group $G$ and $E/F$ regular that has all the Galois extensions of $F$ with…

Let $\mathcal{C}$ be an irreducible plane curve of $\text{PG}(2,\mathbb{K})$ where $\mathbb{K}$ is an algebraically closed field of characteristic $p\geq 0$. A point $Q\in \mathcal{C}$ is an inner Galois point for $\mathcal{C}$ if the…

A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.

This paper describes a class of Artin-Schreier curves, generalizing results of Van der Geer and Van der Vlugt to odd characteristic. The automorphism group of these curves contains a large extraspecial group as a subgroup. Precise knowledge…

This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative…

We consider isomorphisms and automorphisms of quantum groups. Let $k$ be a field and suppose $p, q\in k^*$ are not roots of unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_2)$ and $U_p(\mathfrak{sl}_2)$ over a field $k$ are…

We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual one. We…

This paper is on the inverse parameterized differential Galois problem. We show that surprisingly many groups do not occur as parameterized differential Galois groups over K(x) even when K is algebraically closed. We then combine the method…

We classify, up to conjugacy, the finite (constant) subgroups G of adjoint absolutely simple algebraic groups of type $A_1$ over an arbitrary field $k$ of characteristic not 2.

In this article, we consider the inverse Galois problem for parameterized differential equations over k((t))(x) with k any field of characteristic zero and use the method of patching over fields due to Harbater and Hartmann. As an…

We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible…

For a classical group $G$ over a field $F$ together with a finite-order automorphism $\theta$ that acts compatibly on $F$, we describe the fixed point subgroup of $\theta$ on $G$ and the eigenspaces of $\theta$ on the Lie algebra…

The purpose of this paper is to propose an efficient method to compute the automorphism group of an arbitrary hyperelliptic function field (genus>1) over a given ground field of characteristic >2 as well as over its algebraic extensions.