On the Adams-Riemann-Roch theorem in positive characteristic

TL;DR

This paper presents a new proof of the Adams-Riemann-Roch theorem for smooth projective morphisms over regular schemes in characteristic p, and addresses an open question by K"ock.

Contribution

It provides a novel proof of the Adams-Riemann-Roch theorem in positive characteristic and offers partial answers to existing open questions.

Findings

New proof of Adams-Riemann-Roch theorem in characteristic p

Partial resolution of K"ock's question

Applicable to regular schemes quasi-projective over _p

Abstract

We give a new proof of the Adams-Riemann-Roch theorem for a smooth projective morphism $X\to Y$, in the situation where $Y$ is a regular scheme, which is quasi-projective over $\mF_p$. We also partially answer a question of B. K\"ock.