The C2–spectrum Tmf1(3) and its invertible modules

Hill, Michael; Meier, Lennart

doi:10.2140/agt.2017.17.1953

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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

DOI: 10.2140/agt.2017.17.1953

Abstract

We explore the $C_{2}$ –equivariant spectra ${Tmf}_{1} (3)$ and ${TMF}_{1} (3)$ . In particular, we compute their $C_{2}$ –equivariant Picard groups and the $C_{2}$ –equivariant Anderson dual of ${Tmf}_{1} (3)$ . This implies corresponding results for the fixed-point spectra ${TMF}_{0} (3)$ and ${Tmf}_{0} (3)$ . 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

References

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/

Volume 17, issue 4 (2017)