Wojciech J. Gajda

Abstract: The Neron height pairing is a canonical real-valued pairing between divisors of degree zero and disjoint support on a compact Riemann surface. It serves as an archimedean contribution to the global canonical (Neron-Tate) height pairing between points on the jacobian of a curve over a number field. We review joint work with David Holmes in which we determined the asymptotic behavior of the Neron height pairing on a family of degenerating Riemann surfaces parametrized by an algebraic curve. It turns out that the limit behavior is controlled by a non-archimedean (Q-valued) analogue of the Neron pairing. If time permits we discuss extensions of this result to the Arakelov-Green's pairing between points on a Riemann surface.