The Lubin-Tate stack and Gross-Hopkins duality

Abstract

Morava $E$-theory $E$ is an $E_{\infty }$-ring with an action of the Morava stabilizer group $\Gamma$. We study the derived stack $\mathrm{Spf}E/\Gamma$. Descent-theoretic techniques allow us to deduce a theorem of Hopkins-Mahowald-Sadofsky on the $K(n)$-local Picard group, as well as a recent result of Barthel-Beaudry-Stojanoska on the Anderson duals of higher real $K$-theories.

23 pages; fixed numerous typos and errors

References in corpus (3)

• The Picard group of topological modular forms via descent theory
• K-theory, reality, and duality
• Finite subgroups of extended Morava stabilizer groups

Cited by in corpus (2)

• The Devinatz-Hopkins Theorem via Algebraic Geometry
• Moduli stack of oriented formal groups and periodic complex bordism