Volume 14, issue 2 (2010)

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Structured ring spectra and displays

Tyler Lawson

Geometry & Topology 14 (2010) 1111–1127
Abstract

We combine Lurie’s generalization of the Hopkins–Miller theorem with work of Zink–Lau on displays to give a functorial construction of even-periodic ${E}_{\infty }$ ring spectra $E$, concentrated in chromatic layers $2$ and above, associated to certain $n×n$ invertible matrices with coefficients in the Witt ring of ${\pi }_{0}\left(E\right)$. This is applied to examples related to Lubin–Tate and Johnson–Wilson spectra. We also give a Hopf algebroid presentation of the moduli of $p$–divisible groups of height greater than or equal to $2$.

Keywords
structured ring spectrum, p-divisible group, display
Mathematical Subject Classification 2000
Primary: 55P42
Secondary: 55N22, 55P43, 14L05