This volume contains the written account of the Bonn Seminar on Arithmetic Geometry 2003/2004. It gives a coherent exposition of the theory of intersections of modular correspondences. The focus of the seminar is the formula for the intersection number of arithmetic modular correspondences due to Gross and Keating. Other topics treated are Hurwitz's theorem on the intersection of modular correspondences over the field of complex numbers and the relation of the arithmetic intersection numbers to Fourier coefficients of Siegel-Eisenstein series.

Also included is background material on one-dimensional formal groups and their endomorphisms and on quadratic forms over the ring of $p$-adic integers.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

• G. Vogel -- Modular polynomials
• U. Görtz -- A sum of representation numbers
• U. Görtz -- Arithmetic intersection numbers
• T. Wedhorn -- The genus of the endomorphisms of a supersingular elliptic curve
• V. Meusers -- Lubin-Tate formal groups
• E. Viehmann and K. Ziegler -- Formal moduli of formal $\mathcal{O}_K$-modules
• S. Wewers -- Canonical and quasi-canonical liftings
• V. Meusers -- Canonical and quasi-canonical liftings in the split case
• E. Viehmann -- Lifting endomorphisms of formal $\mathcal{O}_K$-modules
• I. Vollaard -- Endomorphisms of quasi-canonical lifts
• I. Bouw -- Invariants of ternary quadratic forms
• M. Rapoport -- Deformations of isogenies of formal groups
• S. Wewers -- An alternative approach using ideal bases
• T. Wedhorn -- Calculation of representation densities
• M. Rapoport and T. Wedhorn -- The connection to Eisenstein series
• Index