Related papers: Cyclic abelian varieties over finite fields in ord…

Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction of $E$ modulo that prime has rational cyclic isogeny of fixed degree, we can ask if this forces $E$ to have a cyclic isogeny of that degree…

Let $A$ be an abelian variety over $\mathbb{F}_q$. Let $h_A(t)$ be the characteristic polynomial of $A$. Rybakov showed that if $h_A(t)$ is squarefree and $G$ is any finite group with $|G| = h_A(1)$, then $G = A'(\mathbb{F}_q)$ for some…

Let A_K be an abelian variety over a discrete valuation field K. Let A be the Neron model of A_K over the ring of integers O_K of K and A_k its special fibre. We study the set of rational points of the group of components \phi_A of A_k. In…

We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular $\mathbb C$ or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: For the Zilber fields, the only pointwise…

In this paper, we study a question of Colliot-Th\'el\`ene and Iyer concerning the existence of rational sections in families of homogeneous spaces over an abelian variety, after base change by a suitable \'etale isogeny of the abelian…

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…

We show that any soluble group $G$ of type Bredon-$\FP_{\infty}$ with respect to the family of all virtually cyclic subgroups such that centralizers of infinite order elements are of type $\FP_{\infty}$ must be virtually cyclic. To prove…

Let $W$ be a Coxeter group whose proper parabolic subgroups are finite. According to Theorem~1.12 of [1], if the module of a finite $W$-digraph $\Gamma$ is isomorphic to the module of a $W$-graph over $Q$, then $\Gamma$ is acyclic. We…

This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed field, in which the image of at least one element is…

Associated to an abelian variety over a number field are several interesting and related groups: the motivic Galois group, the Mumford-Tate group, $\ell$-adic monodromy groups, and the Sato-Tate group. Assuming the Mumford-Tate conjecture,…

We give a simple proof of the well-known fact: any group of n elements is cyclic if and only if n and \phi(n) are coprime. This note is accessible for students familiar with permutations and basic number theory. No knowledge of abstract…

We discuss two properties of an abelian variety, namely, being a direct summand in a product of Jacobians and the weaker property of being "split". We relate the first property to the integral Hodge conjecture for curve classes on abelian…

We prove the existence of abelian varieties not isogenous to Jacobians over characterstic $p$ function fields. Our methods involve studying the action of degree $p$ Hecke operators on hypersymmetric points, as well as their effect on the…

We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…

We introduce the concept of the modularity of an abelian variety defined over the rational number field extending the modularity of an elliptic curve. We discuss the modularity of an abelian variety over the rational number field. We…

Let $X$ be an affine, simplicial toric variety over a field. Let $G_0$ denote the Grothendieck group of coherent sheaves on a Noetherian scheme and let $F^1G_0$ denote the first step of the filtration on $G_0$ by codimension of support.…

Let $K$ be a finite extension of the $p$-adic numbers $\mathbb Q_p$ with ring of integers $\mathcal O_K$, $\mathcal X$ a regular scheme, proper, flat, and geometrically irreducible over $\mathcal O_K$ of dimension $d$, and $\mathcal X_K$…

We study actions by filtered automorphisms on classical generalized Weyl algebras (GWAs). In the case of a defining polynomial of degree two, we prove that the fixed ring under the action of a finite cyclic group of filtered automorphisms…

We produce an explicit family of totally real cyclic quartic polynomials that are monogenic in many cases and, if the $abc$ conjecture holds, generate distinct monogenic quartic fields infinitely often. Additional families (also…

Consider a pseudogroup on (C,0) generated by two local diffeomorphisms having analytic conjugacy classes a priori fixed in Diff(C,0). We show that a generic pseudogroup as above is such that every point has (possibly trivial) cyclic…