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The \(C_2\)-spectrum \(\mathrm{Tmf}_1(3)\) and its invertible modules. (English) Zbl 1421.55002
Summary: We explore the \(C_2\)-equivariant spectra \(\operatorname{Tmf}_1(3)\) and \(\operatorname{TMF}_1(3)\). In particular, we compute their \(C_2\)-equivariant Picard groups and the \(C_2\)-equivariant Anderson dual of \(\operatorname{Tmf}_1(3)\). This implies corresponding results for the fixed-point spectra \(\operatorname{TMF}_0(3)\) and \(\operatorname{Tmf}_0(3)\). Furthermore, we prove a real Landweber exact functor theorem.

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