2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61456We show that a conjectural extension of a fixed point formula in Arakelov geometry implies results about a tautological subring in the arithmetic Chow ring of bases of abelian schemes. Among the results are an Arakelov version of the Hirzebruch proportionality principle and a formula for a critical power of $\hat c_1$ of the Hodge bundle.15 pagesAlgebraic GeometryDifferential Geometry14G40; 58J52; 20G05; 20G10; 14M17text