An arithmetic Riemann-Roch theorem in higher degrees

TL;DR

This paper establishes an arithmetic analogue of the Grothendieck-Riemann-Roch theorem within Arakelov geometry, extending classical results to higher degrees and providing new tools for arithmetic intersection theory.

Contribution

It introduces a higher-degree arithmetic Riemann-Roch theorem in Arakelov geometry, expanding the scope of classical algebraic geometry results.

Findings

Proved an arithmetic Riemann-Roch theorem in higher degrees

Extended classical Grothendieck-Riemann-Roch to Arakelov setting

Provided new methods for arithmetic intersection calculations

Abstract

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.