Real orientations of Lubin–Tate spectra

Abstract

Abstract We show that Lubin–Tate spectra at the prime 2 are Real oriented and Real Landweber exact. The proof is by application of the Goerss–Hopkins–Miller theorem to algebras with involution. For each height n, we compute the entire homotopy fixed point spectral sequence for $$E_n$$

E n

with its $$C_2$$

C 2

-action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these $$C_2$$

C 2

-fixed points.