The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms

TL;DR

This paper extends the arithmetic Grothendieck-Riemann-Roch theorem to general projective morphisms between regular arithmetic varieties, broadening its applicability beyond smooth morphisms using generalized analytic torsion.

Contribution

It generalizes the classical theorem to non-smooth projective morphisms by employing the theory of generalized analytic torsion.

Findings

The theorem now applies to a wider class of morphisms.

New techniques involving generalized analytic torsion are developed.

The results enhance the understanding of arithmetic characteristic classes.

Abstract

The classical arithmetic Grothendieck-Riemann-Roch theorem can be applied only to projective morphisms that are smooth over the complex numbers. In this paper we generalize the arithmetic Grothendieck-Riemann-Roch theorem to the case of general projective morphisms between regular arithmetic varieties. To this end we rely on the theory of generalized analytic torsion developed by the authors.