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

## TL;DR

This paper employs descent methods to resolve the homotopy limit problem for Hermitian K-theory over certain schemes and computes the cellular Picard group of 2-complete Hermitian K-theory over the complex spectrum, revealing that invertible spectra are just suspensions of the tensor unit.

## Contribution

It introduces descent theoretic techniques to solve the homotopy limit problem and computes the cellular Picard group for Hermitian K-theory, providing new insights into its structure.

## Key findings

- Resolved the homotopy limit problem for Hermitian K-theory over specific schemes.
- Computed the cellular Picard group of 2-complete Hermitian K-theory over complex spectra.
- Showed that the only invertible cellular spectra are suspensions of the tensor unit.

## Abstract

We use descent theoretic methods to solve the homotopy limit problem for Hermitian $K$-theory over quasi-compact and quasi-separated base schemes. 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.