We propose a conjecture combining the Mordell-Lang conjecture with an important special case of the André-Oort conjecture, and explain how existing results imply evidence for it. Mathematics Subject Classification: 14G35, 14K12 (11F32, 11F72, 11G15, 11G18)

We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton–Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.

This is an extended version of the talk I gave at the summer school in Göttingen in July 2007. We discuss the Mordell-Weil Sieve and some applications.

We prove certain uniform versions of the Mordell Conjecture and of the Shafarevich Conjecture for curves over function fields and their rational points.

We introduce finite and symmetric Mordell–Tornheim type of multiple zeta values give a new approach to the Kaneko–Zagier conjecture stating that satisfy same relations.

We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let φ be a rational function with no superattracting periodic points other than exceptional points. If the coefficients of φ are algebraic, we show that the orbit of a point outside the union of proper preperiodic subvarieties of (P) has only finite intersection with any curve contained in (...

In this paper we investigate divisibility properties of two families of sequences in the Mordell–Weil group of elliptic curves over number fields without complex multiplication. We also consider more general groups of Mordell–Weil type. M. Ward ([W], Theorem 1.) proved that a linear integral recurring sequence of order two which is not nontrivially degenerate has an infinite number of distinct ...

Let X A be a reduced, irreducible, closed subvariety of a semiabelian variety A over an algebraically closed eld k. We would like to study the structure of such an X. Our point of departure is arithmetic: motivated by Lang's conjectures 15, 17, 16], as manifested by the theorems of Faltings 6, 7] and Vojta 27], we study the Mordell exceptional locus: that is, the union of translated positive di...