Related papers: Abelian Varieties with Prescribed Embedding Degree

The $2M$-boson representations of KP hierarchy are constructed in terms of $M$ mutually independent two-boson KP representations for arbitrary number $M$. Our construction establishes the multi-boson representations of KP hierarchy as…

In a remarkable article Ribet showed how to attach rational $2$-dimensional representations to elliptic ${\mathbb Q}$-curves. An abelian variety $A$ is a (weak) $K$-variety if it is isogenous to all of its $\text{Gal}_K$-conjugates. In this…

We show that, with some technical conditions, an abelian category can be embedded into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.

More than four decades ago, Eisenbud, Khim\v{s}ia\v{s}vili, and Levine introduced an analogue in the algebro-geometric setting of the notion of local degree from differential topology. Their notion of degree, which we call the EKL-degree,…

In this paper, using a generalization of the notion of Prym variety for covers of quasi-projective varieties, we prove a structure theorem for the Mordell-Weil group of the abelian varieties over function fields that are twists of Abelian…

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A = kQ/I. Let QGr A denote…

We classify principal bundles over anti-affine schemes with affine and commutative structural group. We show that this yields the classification of quasi-abelian varieties over a field k (i.e., group k-schemes with no non constant global…

For an abelian variety $A$ over a number field we study bounds depending only on the dimension of $A$ for the minimal degree $d(A)$ of a field extension over which $A$ acquires semi-stable reduction. We first compute $d(A)$ in terms of the…

We study abelian varieties $A$ with multiplication by a totally indefinite quaternion algebra over a totally real number field and give a criterion for the existence of principal polarizations on them in pure arithmetic terms. Moreover, we…

We classify group schemes in terms of their Cartier modules. We also prove the equivalence of different definitions of the tangent space and the dimension for these group schemes; in particular, the minimal dimension of a formal group law…

Let k be a field and f be a Siegel modular form of weight h \geq 0 and genus g>1 over k. Using f, we define an invariant of the k-isomorphism class of a principally polarized abelian variety (A,a)/k of dimension g. Moreover when (A,a) is…

One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. We provide explicit bounds on the primes appearing in the denominators of…

Let $m,n,d > 1$ be integers such that $n=md$. In this paper, we present an efficient change of level algorithm that takes as input $(B, \mathscr{M}, \Theta_\mathscr{M})$ a marked abelian variety of level $m$ over the base field $k$ of odd…

For every number field $k$, we construct an affine algebraic surface $X$ over $k$ with a Zariski dense set of $k$-rational points, and a regular function $f$ on $X$ inducing an injective map $X(k)\to k$ on $k$-rational points. In fact,…

We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type. More precisely, we first build on Kisin's work to construct integral canonical models over rings of integers of number…

In this paper, we study in the context of quantum vertex algebras a certain Clifford-like algebra introduced by Jing and Nie. We establish bases of PBW type and classify its $\mathbb N$-graded irreducible modules by using a notion of Verma…

Let $kE$ denote the group algebra of an elementary abelian $p$-group of rank $r$ over an algebraically closed field of characteristic $p$. We investigate the functors $\mathcal{F}_i$ from $kE$-modules of constant Jordan type to vector…

Let $F$ be a totally real number field of class number one, and let $K$ be a CM-field with $F$ as its maximal real subfield. For each positive integer $N$, we construct a class group of certain binary quadratic forms over $F$ which is…

Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired…

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…