The homotopy limit problem and the cellular Picard group of Hermitian K-theory

Abstract

We use descent theoretic methods to solve the homotopy limit problem for Hermitian $K$-theory over very general Noetherian base schemes, assuming that the natural map from Hermitian $K$-theory to algebraic $K$-theory is a map of commutative motivic ring spectra. As another application of these descent theoretic methods, we compute the cellular Picard group of 2-complete Hermitian $K$-theory over $\mathop{Spec}(\mathbb{C})$, showing that the only invertible cellular spectra are suspensions of the tensor unit.