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

1705.02810May 8, 2017v4: results made unconditional, assumptions on base scheme weakened. Version to appear in Annals of K-theory

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

Drew Heard

Algebraic Topology K-Theory and Homology

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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.

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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 Spec(C), showing that the only invertible cellular spectra are suspensions of the tensor unit.

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The paper addresses: The homotopy limit problem and the cellular Picard group of Hermitian K-theory.
We use descent theoretic methods to solve the homotopy limit problem for Hermitian K-theory over quasi-compact and quasi-separated base schemes.

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