Adic finiteness: Bounding homology and applications

Abstract

Abstract. We prove a versions of amplitude inequalities of Iversen, Foxby and Iyengar, and Frankild and Sather-Wagstaff that replace finite generation conditions with adic finiteness conditions. As an application, we prove that a local ring R of prime characteristic is regular if and only if for some proper ideal b the derived local cohomology complex RΓ b (R) has finite flat dimension when viewed through some positive power of the Frobenius endomorphism.