Vol. 6, No. 1, 2021

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The homotopy limit problem and the cellular Picard group of Hermitian $K\mkern-2mu$-theory

Drew Heard

Vol. 6 (2021), No. 1, 137–156
Abstract

We use descent theoretic methods to solve the homotopy limit problem for Hermitian K-theory over quasicompact and quasiseparated base schemes. As another application of these descent theoretic methods, we compute the cellular Picard group of 2-complete Hermitian K-theory over  Spec(), showing that the only invertible cellular spectra are suspensions of the tensor unit.

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Keywords
homotopy limit, Hermitian $K\mkern-2mu$-theory, Picard group, motivic homotopy
Mathematical Subject Classification
Primary: 14F42
Secondary: 19G38, 55P42
Milestones
Received: 4 June 2020
Revised: 17 August 2020
Accepted: 17 September 2020
Published: 8 July 2021
Authors
Drew Heard
Department of Mathematical Sciences
Norwegian University of Science and Technology
Trondheim
Norway