INTERCITY SEMINAR ON ARAKELOV GEOMETRY -- A conjectural relative height pairing
Ponente: Damian Rössler (Universidad de Oxford)Fecha: miércoles 14 de septiembre de 2022 - 10:15 - 11:15 Lugar: Aula Gris 2, ICMAT
In a recent article, Tamas Szamuely and the speaker defined a geometric height pairing for varieties defined over the function field of a smooth variety defined over an algebraically closed field. This pairing has values in the second l-adic cohomology group of a model of the function field and conjecturally the pairing should arise from a “motivic” pairing with values in the rational Picard group of the model. This leads to some speculation on the possible existence of a similar pairing for varieties defined over function fields of arithmetic varieties, which would have values in an Arakelov Picard group. I will discuss some special cases of this conjecture and I will explain what analytic problems arise when one tries to make it more precise. This is very much work in progress.
(Partially joint with Tamás Szamuely)