Abstract

In his celebrated paper on height pairings, Beilinson has defined a height pairing for homologically trivial algebraic cycles on varieties defined over the function field of a curve. A few years ago, Damian Roessler and I have extended Beilinson's construction to varieties defined over a function field of a base variety B of arbitrary dimension. The values of our pairing are not numbers any more but elements in the second cohomology group of B. We have conjectured that this pairing is of geometric origin, i.e. comes from a pairing with values in the Picard group of B (tensored with Q). In recent work with P. Brosnan and G. Pearlstein, we verify this conjecture in the case when the base field is C. In my lecture I shall explain the evolution of the idea of geometric height pairings and give some ideas of our construction.