Fppf descent and localizing subcategories for algebraic spaces

Abstract

We prove descendability for fppf covers of quasi-compact quasi-separated algebraic spaces. Consequently, we show that point-generatedness is detectable along fppf covers. Moreover, we classify $\otimes$-localizing subcategories of the derived category of complexes with quasi-coherent cohomology on point-generated algebraic spaces in terms of subsets of the underlying topology.

improved results for fppf descent, restructure to algebraic spaces, sharper exposition