The stable Adams operations on Hermitian K-theory

TL;DR

This paper establishes a $ ext{lambda}$-ring structure on Hermitian $K$-theory and defines stable Adams operations, providing new tools for understanding Hermitian bundles and their algebraic properties.

Contribution

It introduces a $ ext{lambda}$-ring structure on Hermitian $K$-theory and constructs stable Adams operations, advancing the algebraic framework of Hermitian bundles.

Findings

$ ext{lambda}$-ring structure on $GW^0(X) igoplus GW^2(X)$

Definition of stable Adams operations on Hermitian $K$-theory

Computation of ternary laws in Hermitian $K$-theory

Abstract

We prove that exterior powers of (skew-)symmetric bundles induce a $\lambda$-ring structure on the ring $GW^0(X) \oplus GW^2(X)$, when $X$ is a scheme where $2$ is invertible. Using this structure, we define stable Adams operations on Hermitian $K$-theory. As a byproduct of our methods, we also compute the ternary laws associated to Hermitian $K$-theory.