Faithfully flat ring maps are not descendable

It is an important foundational result in algebraic geometry that the 2 2 -category of quasi-coherent modules fibered over the category of commutative rings satisfies descent with respect to the fqpc topology. More recently, Akhil Mathew and Jacob Lurie introduced an ∞ ∞ -categorical version of this result for module spectra using the notion of descendable E ∞ E∞ -ring maps . In this paper, we will construct a faithfully flat algebra over the infinite polynomial ring on an algebraically closed field that is not descendable.