Algebraic & Geometric Topology

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

Michael Hill and Lennart Meier

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

Permanent link to this document
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

Keywords
topological modular forms real homotopy theory Picard group Anderson duality

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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