The $C_2$-spectrum $Tm{f}_1(3)$ and its invertible modules

Abstract

We explore the $C_2$-equivariant spectra $Tm{f}_1(3)$ and $TM{F}_1(3)$. In particular, we compute their $C_2$-equivariant Picard groups and the $C_2$-equivariant Anderson dual of $Tm{f}_1(3)$. This implies corresponding results for the fixed point spectra $TM{F}_0(3)$ and $Tm{f}_0(3)$. Furthermore, we prove a Real Landweber exact functor theorem.

Final version to appear in AGT. 51 pages

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