The arithmetic Siegel-Weil formula is a conjectural formula, due to Kudla, that predicts relations between arithmetic heights of certain "special” cycles on Shimura varieties and derivatives of Eisenstein series.

In this talk, we will focus on zero-dimensional Shimura varieties attached to rational tori; our main result is an abstract version of the arithmetic Siegel-Weil formula in this case, which in particular offers a somewhat more conceptual point of view on prior results in the literature.