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arXiv · 1810.06651

Constructing the determinant sphere using a Tate twist

Tobias Barthel·Agnès Beaudry·Paul G. Goerss·Vesna Stojanoska
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Abstract

Following an idea of Hopkins, we construct a model of the determinant sphere $S\langle det \rangle$ in the category of $K(n)$-local spectra. To do this, we build a spectrum which we call the Tate sphere $S(1)$. This is a $p$-complete sphere with a natural continuous action of $\mathbb{Z}_p^\times$. The Tate sphere inherits an action of $\mathbb{G}_n$ via the determinant and smashing Morava $E$-theory with $S(1)$ has the effect of twisting the action of $\mathbb{G}_n$. A large part of this paper consists of analyzing continuous $\mathbb{G}_n$-actions and their homotopy fixed points in the setup of Devinatz and Hopkins.

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BibTeXRIS

Tobias Barthel, Agnès Beaudry, Paul G. Goerss, Vesna Stojanoska. 2021-09-13. Constructing the determinant sphere using a Tate twist. https://arxiv.org/abs/1810.06651

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