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

We explore the C2–equivariant spectra Tmf1(3) and TMF1(3). In particular, we compute their C2–equivariant Picard groups and the C2–equivariant Anderson dual of Tmf1(3). This implies corresponding results for the fixed-point spectra TMF0(3) and Tmf0(3). Furthermore, we prove a real Landweber exact functor theorem.

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topological modular forms, real homotopy theory, Picard group, Anderson duality
Mathematical Subject Classification 2010
Primary: 55N34, 55P42
Received: 3 August 2015
Revised: 4 November 2016
Accepted: 29 November 2016
Published: 3 August 2017
Michael A Hill
Department of Mathematics
University of California, Los Angeles
Box 951555
Los Angeles, CA 90095-1555
United States
Lennart Meier
Mathematisches Institut
University of Bonn
Endenicher Allee 60
D-53115 Bonn