On the Order of Certain Characteristic Classes of the Hodge Bundle of Semi-Abelian Schemes

We give a new proof of the fact that the even terms (of a multiple of) the Chern character of the Hodge bundles of semi-abelian schemes are torsion classes in Chow theory and we give explicit bounds for almost all the prime powers appearing in their order. These bounds appear in the numerators of modified Bernoulli numbers. We also obtain similar results in an equivariant situation.