Algebraic & Geometric Topology

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

Michael Hill and Lennart Meier

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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.

Article information

Algebr. Geom. Topol., Volume 17, Number 4 (2017), 1953-2011.

Received: 3 August 2015
Revised: 4 November 2016
Accepted: 29 November 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55N34: Elliptic cohomology 55P42: Stable homotopy theory, spectra

topological modular forms real homotopy theory Picard group Anderson duality


Hill, Michael; Meier, Lennart. The $C_2$–spectrum $\mathrm{Tmf}_1(3)$ and its invertible modules. Algebr. Geom. Topol. 17 (2017), no. 4, 1953--2011. doi:10.2140/agt.2017.17.1953.

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