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Picard groups and duality for real Morava $E$–theories

Drew Heard, Guchuan Li and XiaoLin Danny Shi

Algebraic & Geometric Topology 21 (2021) 2703–2760
Abstract

We show, at the prime 2, that the Picard group of invertible modules over EnhC2 is cyclic. Here, En is the height n Lubin–Tate spectrum and its C2–action is induced from the formal inverse of its associated formal group law. We further show that EnhC2 is Gross–Hopkins self-dual and determine the exact shift. Our results generalize the well-known results when n = 1.

Keywords
chromatic homotopy, Picard group, Brown–Comenetz, Morava, Gross–Hopkins, real K–theory
Mathematical Subject Classification 2010
Primary: 14C22, 19L99, 55P91, 55U30
Secondary: 55N20, 55P43
References
Publication
Received: 14 November 2018
Revised: 25 November 2019
Accepted: 12 October 2020
Published: 22 November 2021
Authors
Drew Heard
Department of Mathematical Sciences
Norwegian University of Science and Technology
Trondheim
Norway
https://folk.ntnu.no/drewkh/
Guchuan Li
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States
XiaoLin Danny Shi
Department of Mathematics
University of Chicago
Chicago, IL
United States