Related papers: Non-isogenous abelian varieties sharing the same d…

Faltings in 1983 proved that a necessary and sufficient condition for two abelian varieties $A$ and $B$ to be isogenous over a number field $K$ is that the local factors of the L-series of $A$ and $B$ are equal for almost all primes of $K$…

A simple abelian variety $A$ defined over a number field $k$ is called of $\mathrm{GL}_n$-type if there exists a number field of degree $2\dim(A)/n$ which is a subalgebra of $\mathrm{End}^0(A)$. We say that $A$ is genuinely of…

We define an integer-valued invariant of special cube complexes called the genus, and prove that having genus one characterizes special cube complexes with abelian fundamental group. Using the genus, we obtain a new proof that the…

We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary…

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective…

In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by combining Tate's classification of the endomorphism…

We construct the duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to each other by first-order (self-)duality equations that follow from…

Let us consider an abelian variety defined over $\mathbb{Q_{\ell}}$ with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the $\ell$-torsion points of the…

By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and…

We consider the distribution of p-power group schemes among the torsion of abelian varieties over finite fields of characteristic p, as follows. Fix natural numbers g and n, and let $\xi$ be a non-supersingular principally quasipolarized…

Using generalized field strength tensors for non-Abelian tensor gauge fields one can explicitly construct all possible Lorentz invariant quadratic forms for rank-4 non-Abelian tensor gauge fields and demonstrate that there exist only two…

Let $A$ be a semistable abelian variety defined over ${\bf Q}$ with bad reduction only at one prime $p$. Let $L= {\bf Q}(A[\ell])$ be the $\ell$-division field of $A$ for a prime $\ell$ not equal to $p$ and let $F={\bf Q}(\mu_\ell)$ be the…

In this paper we show that if $\phi_{i}:A_{i}\rightarrow{A}$ is a semisimple pointed $K$-rational $\ell$-isogeny graph of order $n$ for a prime $\ell$, then the group of $\ell$-torsion points $A[\ell](\overline{K})$ contains a subspace of…

Let $K$ be a number field. We present several new finiteness results for isomorphism classes of abelian varieties over $K$ whose $\ell$-power torsion fields are arithmetically constrained for some rational prime $\ell$. Such arithmetic…

For an abelian variety $A$ over a number field $K$, we define the set of Tamagawa torsors of $A$ at a prime $v$ of $K$ to be the set of principal homogeneous spaces of $A$ over the completion $K_v$ of $K$ at $v$ that are split by an…

The aim of this paper is to find all algebraic threefolds admitting quasi-regular Poisson structure. There are three types of such varieties: abelian varieties, smooth flat conic bundles over abelian surfaces and quotients of the product of…

We compare general inequalities between invariants of number fields and invariants of abelian varieties over number fields. On the number field side, we remark that there is only a finite number of non-CM number fields with bounded…

We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that…

We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure…

The results in this paper imply that for every number field F and positive integer r, there exists an F-isogeny class of abelian varieties such that r divides the degree of every F-polarization on every abelian variety in the isogeny class.