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 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 $\mathrm{Spec}(\mathbb{C})$, showing that the only invertible cellular spectra are suspensions of the tensor unit.

v4: results made unconditional, assumptions on base scheme weakened. Version to appear in Annals of K-theory

References in corpus (6)

• Higher Topos Theory
• Local duality in algebra and topology
• C_2-equivariant stable homotopy from real motivic stable homotopy
• Cdh descent in equivariant homotopy K-theory
• Brauer groups and Galois cohomology of commutative ring spectra
• Local duality for structured ring spectra

Cited by in corpus (1)

• Coassembly is a homotopy limit map