Hirzebruch proportionality principle in Arakelov geometry

 
K. Köhler

 
 
  We describe a tautological subring in the arithmetic Chow ring of bases of abelian schemes of relative dimension d. Among the results are an Arakelov version of the Hirzebruch proportionality principle and a purely analytical formula for the global height of complete bases of dimension d(d-1)/2.