Exotic periodic phenomena in the cohomology of the moduli stack of one‐dimensional formal group laws

We describe some periodic structure in the cohomology of the moduli stack of one‐dimensional formal group laws, also known as the ‐page of the classical Adams–Novikov spectral sequence. This structure is distinct from the familiar ‐periodicities, and it displays interesting number‐theoretic properties. Our techniques involve the ‐motivic Adams spectral sequence, and we obtain analogous periodic structure in ‐motivic stable homotopy.