## Algebraic & Geometric Topology

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

#### Abstract

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

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

Dates
Revised: 4 November 2016
Accepted: 29 November 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841434

Digital Object Identifier
doi:10.2140/agt.2017.17.1953

Mathematical Reviews number (MathSciNet)
MR3685599

Zentralblatt MATH identifier
06762682

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1510841434

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