Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Thursday, 12 June 2008

Damian Roessler: On the p-adic distance between a torsion point and a curve of genus >1

Abstract:

Let A be an abelian variety defined over C_p (the p-adic "complex" numbers), and V a subvariety of A. A conjecture of Tate and Voloch then states that there exists a constant M > 0 such that for every torsion point T in the complement of V in A, one has distance(T,V) > M. This is proven by Hrushovski and Scanlon when A has a model over Q_p. We shall give an explicit formula for M, valid when V is a curve of genus > 1, A is its jacobian and V is defined over a number field. The constant depends on some analytic and Arakelov-theoretic invariants.