Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence

Using the Landweber–Araki theory of Real cobordism and Real-oriented spectra, we define a Real analogue of the Adams–Novikov spectral sequence. This is a new spectral sequence with a potentially calculable E2-term. It has versions converging to either the Z/2-equivariant or the non-equivariant stable 2-stems. We also construct a Real analogue of the Miller–Novikov ‘algebraic’ spectral sequence.