Related papers: Hilbert irreducibility for abelian varieties over …

We extend the well-known Cassels-Tate dual exact sequence for abelian varieties A over global fields K in two directions: we treat the p-primary component in the function field case, where p is the characteristic of K, and we dispense with…

We revisit generic vanishing results for perverse sheaves with any field coefficients on a complex semi-abelian variety, and indicate several topological applications. In particular, we obtain finiteness properties for the integral…

In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D}d(L) $$ for some $n\geq 1$, is…

Let $X$, $Y$ be closed irreducible subvarieties of an absolutely simple abelian variety of dimension $g$ over a field. If $\dim(X) + \dim(Y) \le g$, we prove that the addition morphism $X \times Y \to X + Y$ is semismall. As a consequence,…

We give an alternative proof to the annihilator of local cohomology in characteristic zero which was proved by Lyubeznik.

We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.

We classify the irreducible Hermitian real variations of Hodge structure admitting an infinitesimal normal function, and draw conclusions for cycle-class maps on families of abelian varieties with a given Mumford-Tate group.

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…

In this paper we prove a characterization of quotients of Abelian varieties by the actions of finite groups that are free in codimension-one via some vanishing conditions on the orbifold Chern classes. The characterization is given among a…

This article contributes to the study of the generic part of the cohomology of Shimura varieties. Under a mild restriction of the characteristic of the coefficient field, we prove a torsion vanishing result for Shimura varieties of abelian…

We extend the usual Hilbert property for varieties over fields to arithmetic schemes over integral domains by demanding the set of near-integral points (as defined by Vojta) to be non-thin. We then generalize results of…

Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of fractions. Under the assumption that K contains all r-th roots of unity for an integer r, we prove that, given an…

Let $A$ be an abelian variety over a field finitely generated over $\mathbb{Q}$. We show that the finiteness of the $\ell$-primary torsion subgroup of the higher Brauer group is a sufficient criterion for the Tate conjecture to hold.…

We prove that the Albanese morphism of any normal proper variety $X$ in positive characteristic satisfying $S^0(X, \omega_X) \neq 0$ and $P_2(X) = 1$ is surjective with connected fibers, adn that $\mathrm{Alb}(X)$ is ordinary. We obtain…

We prove that the algorithm for desingularization of algebraic varieties in characteristic zero of the first two authors is functorial with respect to regular morphisms. For this purpose, we show that, in characteristic zero, a regular…

In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.

We construct, for every prime p, a function field K of characteristic p and an ordinary abelian variety A over K, with no isotrivial factors, that admits an etale self-isogeny of p-power degree. As a consequence, we deduce that there exist…

This paper surveys the methods that have been used to attack the conjecture, still open, that an abelian variety over a characteristic $0$ field with finitely generated Galois group is always of infinite rank.

We prove that the Hilbert scheme of points on a normal quasi-projective surface with at worst rational double point singularities is irreducible.

Using the Rabinowitsch trick, we prove a version of Nullstellensatz over quaternions, which generalizes Hilbert's Nullstellensatz over complex numbers.