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Wojciech J. Gajda

professor of mathematics

Mailing address:
Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Umultowska 87, 61-614 PoznaƄ, POLAND
Office: Collegium Mathematicum, B1-35
Phone: +48 (61) 829 5503
Fax: +48 (61) 829 5315
Email: gajda AT amu DOT edu DOT pl

Research interests:

arithmetic geometry, number theory, algebraic topology, algebraic K-theory

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Robin de Jong, Universiteit Leiden, Netherlands

28.05.2014, 12.00, B1-37

Title: Asymptotics of height pairings on Riemann surfaces

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.