The stable Adams operations on Hermitian K-theory

Jean Fasel (1) , Olivier Haution

1 IF - Institut Fourier

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.

Domaines: Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]; Algèbre commutative [math.AC]

Jean Fasel, Olivier Haution. The stable Adams operations on Hermitian K-theory. 2021. ⟨hal-03470534⟩