A chain morphism for Adams operations on rational algebraic K-theory

TL;DR

This paper constructs a chain morphism in rational algebraic K-theory that induces Adams operations, providing a new algebraic tool for understanding these operations on schemes.

Contribution

It introduces a novel chain morphism connecting two complexes whose homology recovers algebraic K-groups, aligning with known Adams operations.

Findings

The chain morphism induces Adams operations in homology.

The construction applies to any regular noetherian scheme.

It bridges different definitions of Adams operations by Gillet, Soule, and Grayson.

Abstract

For any regular noetherian scheme X and every k>0, we define a chain morphism between two chain complexes whose homology with rational coefficients is isomorphic to the algebraic K-groups of X tensored by the field of rational numbers. It is shown that these morphisms induce in homology the Adams operations defined by Gillet and Soule or the ones defined by Grayson.