Properties of the Beilinson Height Pairing

Abstract

First constructed by Beilinson for curves defined over an algebraically closed field; R\"ossler and Szamuely generalized Beilinson's height pairing to the higher dimensional setting. In this paper we study this pairing and relate it to the intersection product by constructing a new height pairing. We also prove that it satisfies a projection formula matching the one satisfied by the intersection product.