Related papers: Automorphism groups of curves over arbitrary field…

We investigate the Jacobian decomposition of some algebraic curves over finite fields with genus $4$, $5$ and $10$. As a corollary, explicit equations for curves that are either maximal or minimal over the finite field with $p^2$ elements…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

Associated to a finite graph $X$ is its quantum automorphism group $G$. The main problem is to compute the Poincar\'e series of $G$, meaning the series $f(z)=1+c_1z+c_2z^2+...$ whose coefficients are multiplicities of 1 into tensor powers…

In this manuscript, we apply patching methods to give a positive answer to the inverse differential Galois problem over function fields over Laurent series fields of characteristic zero. More precisely, we show that any linear algebraic…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…

We find all the possible torsion groups of $\Q$-curves over quadratic fields and determine which groups appear finitely and which appear infinitely often.

In this paper we introduce a new species of evolution algebras that we call Cayley evolution algebras. We show that if a field $k$ contains sufficiently many elements (for example if $k$ is infinite) then every finite group $G$ is…

In a recent paper of Bhowmick, Skalski and So{\l}tan the notion of a quantum group of automorphisms of a finite quantum group was introduced and, for a given finite quantum group G, existence of the universal quantum group acting on G by…

We call a finite group G ultrasolvable if it has a characteristic subgroup series whose factors are cyclic. It was shown by Durbin--McDonald that the automorphism group of an ultrasolvable group is supersolvable. The converse statement was…

We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K_0 be an arbitrary prime field…

If $C$ is a curve over $\mathbb{Q}$ with genus at least $2$ and $C(\mathbb{Q})$ is empty, then the class of fields $K$ of characteristic 0 such that $C(K) = \varnothing$ has a model companion, which we call $C\mathrm{XF}$. The theory…

Let $X$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \ge 2$ defined over an algebraically closed field $K$ of odd characteristic $p$. Let $Aut(X)$ be the group of all automorphisms of $X$ which fix…

In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This…

We prove that certain fields have the property that their absolute Galois groups are free as profinite groups: the function field of a real curve with no real points; the maximal abelian extension of a 2-variable Laurent series field over a…

We prove automorphy lifting results for geometric representations $\rho:G_F \rightarrow GL_2(\mathcal{O})$, with $F$ a totally real field, and $\mathcal{O}$ the ring of integers of a finite extension of $\mathbb{Q}_p$ with $p$ an odd prime,…

Contents: Rational functions with given monodromy on generic curves (I. Bouw & S. Wewers); Can deformation rings of group representations not be local complete intersections? (T. Chinburg); Lifting an automorphism group to finite…

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

We prove that the isomorphism problem for finitely generated fully residually free groups is decidable. We also show that each finitely generated fully residually free group G has a decomposition that is invariant under automorphisms of G,…

We call a flag variety admissible if its automorphism group is the projective general linear group. (This holds in most cases.) Let $K$ be a field of characteristic $0$, containing all roots of unity. Let the $K$-variety $X$ be a form of an…

For every field $k$ of characteristic zero, we determine the groups that act as automorphisms on a smooth cubic surface over $k$. We also determine the groups that act on $k$-rational, stably $k$-rational, or $k$-unirational smooth cubic…