K3 spectra

Abstract

The notion of a K3 spectrum is introduced in analogy with that of an elliptic spectrum and it is shown that there are ‘enough’ K3 spectra in the sense that for all K3 surfaces X in a suitable moduli stack of K3 surfaces there is a K3 spectrum whose underlying ring is isomorphic to the local ring of the moduli stack in X with respect to the etale topology, and similarly for the ring of formal functions on the formal deformation space.