Let A be a commutative ring and let O be a sheaf of E∞-ring spectra on SpecA such that π0O=OSpecA. Lurie provides a criterion when (SpecA,O) coincides with SpecO(SpecA), namely if the homotopy groups πnO are quasi-coherent sheaves on SpecA and O is

hypercomplete(Spectral Algebraic Geometry, Proposition 1.6.1.1). To get a better understanding why this last condition is really necessary, I would like to know the answer to the following question:Is there an example of sheaf O that is not hypercomplete, but satisfies the other conditions?

By Spectral Algebraic Geometry, Corollary 1.1.3.6, this cannot happen if SpecA is a noetherian space of finite Krull dimension. So a counterexample has to be something big like A=Z[x1,x2,x3,…].

**Answer**

**Attribution***Source : Link , Question Author : Lennart Meier , Answer Author : Community*