On the existence of a compact generator on the derived category of a noetherian formal scheme

摘要

In this paper, we prove that for a noetherian formal scheme fraktur X sign, its derived category of sheaves of modules with quasi-coherent torsion homologies D_(qct)(fraktur X sign) is generated by a single compact object. In an Appendix we prove that the category of compact objects in D_(qct)(fraktur X sign) is skeletally small.