Descent conjecture for perfect and finite projective modules in the noetherian setting

Work in either of the two settings considered in the subsection: the derived analytic or derived algebraic geometric setting with the associated period and Robba rings. Consider perfect, almost perfect, and finite projective modules, together with binary rational coverings. Descent conjecture. In the noetherian situation, descent along binary rational coverings should hold for perfect, almost perfect, and finite projective modules, allowing comparison between sheaves and their global sections. The conjecture is motivated by the need for descent in derived algebraic geometry; the text notes that any verified infinity-descent results in derived algebraic geometry would apply, but supplies no proof or resolution.