# On the higher Riemann-Roch without denominators

## TL;DR

This paper advances the understanding of the higher Riemann-Roch theorem by providing refined formulations applicable to broader classes of schemes and morphisms without requiring smoothness or denominators.

## Contribution

It introduces two new refinements of the higher Riemann-Roch theorem, extending its applicability to regular closed immersions and proper morphisms without smoothness assumptions.

## Key findings

- Refinement for regular closed immersions between noetherian schemes.
- Refinement for the relative cohomology of proper morphisms.
- No smoothness assumptions needed for these refinements.

## Abstract

We prove two refinements of the higher Riemann-Roch without denominators: a statement for regular closed immersions between arbitrary finite dimensional noetherian schemes, with no smoothness assumptions, and a statement for the relative cohomology of a proper morphism.