Volume 17, issue 4 (2017)

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The $C_2$–spectrum $\mathrm{Tmf}_1(3)$ and its invertible modules

Michael A Hill and Lennart Meier

Algebraic & Geometric Topology 17 (2017) 1953–2011
Abstract

We explore the ${C}_{2}$–equivariant spectra ${Tmf}_{1}\left(3\right)$ and ${TMF}_{1}\left(3\right)$. In particular, we compute their ${C}_{2}$–equivariant Picard groups and the ${C}_{2}$–equivariant Anderson dual of ${Tmf}_{1}\left(3\right)$. This implies corresponding results for the fixed-point spectra ${TMF}_{0}\left(3\right)$ and ${Tmf}_{0}\left(3\right)$. Furthermore, we prove a real Landweber exact functor theorem.

Keywords
topological modular forms, real homotopy theory, Picard group, Anderson duality
Mathematical Subject Classification 2010
Primary: 55N34, 55P42
Publication
Received: 3 August 2015
Revised: 4 November 2016
Accepted: 29 November 2016
Published: 3 August 2017
Authors
 Michael A Hill Department of Mathematics University of California, Los Angeles Box 951555 Los Angeles, CA 90095-1555 United States http://math.ucla.edu/~mikehill Lennart Meier Mathematisches Institut University of Bonn Endenicher Allee 60 D-53115 Bonn Germany http://www.math.uni-bonn.de/people/lmeier/