Related papers: Hilbert irreducibility for abelian varieties over …

A proof of freeness of the commutator subgroup of the fundamental group of a smooth irreducible affine curve over a countable algebraically closed field of nonzero characteristic. A description of the abelianizations of the fundamental…

We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…

We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject only to the condition that the irreducible components of…

Shimura proved that each principally polarized abelian variety over $\mathbf{C}$ admits a unique factorization into irreducible principally polarized abelian varieties. We give an exposition of his result, and generalize to an arbitrary…

An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.

Let $F$ be a global function field of characteristic $p>0$, $K/F$ an $\ell$-adic Lie extension ($\ell\neq p$) and $A/F$ an abelian variety. We provide Euler characteristic formulas for the $Gal(K/F)$-module $Sel_A(K)_\ell$.

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…

In this paper we discuss applications of our earlier work in studying certain Galois groups and splitting fields of rational functions in $\mathbb Q\left(X_0(N)\right)$ using Hilbert's irreducibility theorem and modular forms. We also…

In this paper, we prove the geometric Bombieri-Lang conjecture for projective varieties which have finite morphisms to abelian varieties of trivial traces over function fields of characteristic 0. The proof is based on the idea of…

We prove that the standard conjecture of Hodge type holds for powers of abelian threefolds. Along the way, we also prove the conjecture for powers of simple abelian variety of prime dimension over finite fields, and in other related cases…

The biduality and reflexivity theorems are known to hold for projective varieties defined over fields of characteristic zero, and to fail in positive characteristic. In this article, we construct a notion of reflexivity and biduality in…

In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field $\mathbb{F}_q$ whose characteristic polynomial (of Frobenius) is square-free and of abelian varieties defined over the prime field…

A celebrated theorem of Bogomolov asserts that the $\ell$-adic Lie algebra attached to the Galois action on the Tate module of an abelian variety over a number field contains all homotheties. This is not the case in characteristic $p$: a…

A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang in algebraic dynamics is here established: if $X$ is a projective variety over an algebraically closed field of characteristic zero which admits a global algebraic…

Let $A$ and $B$ be abelian varieties defined over the function field $k(S)$ of a smooth algebraic variety $S/k.$ We establish criteria, in terms of restriction maps to subvarieties of $S,$ for existence of various important classes of…

In an earlier paper the author proved one divisibility of Perrin- Riou's Iwasawa main conjecture for Heegner points on elliptic curves. In the present paper, that result is generalized to abelian varieties of GL2-type (i.e. abelian…

Given a field $k$ of characteristic zero and an indeterminate $T$, the main topic of the paper is the construction of specializations of any given finite extension of $k(T)$ of degree $n$ that are degree $n$ field extensions of $k$ with…

We describe an inductive approach most appropriate for abelian varieties with an action of an imaginary quadratic field.