This book, which is a result of a collective effort of the Bonn seminar on arithmetic geometry 2003/04, gives a thorough account of the work of Gross and Keating on (proper) triple intersections of arithmetic Hecke correspondences on the arithmetic threefold Spec Z[j,j’] and their relation to Fourier coefficients of the central derivative of a suitable Siegel-Eisenstein series (a special instance of “Kudla’s programme”). This is a very pleasant introduction to an important topic in contemporary arithmetic geometry, which also covers some useful background material on supersingular elliptic curves, deformation theory of one-dimensional formal groups and quadratic forms over p-adic integers.

Reviewer:

jnek