Reflexivity and ring homomorphisms of finite flat dimension
  In this paper we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings. One primary focus is the descent of these properties over ring homomorphisms of finite flat dimension, presented in terms of inequalities between generalized G-dimensions. Most of these results are new even when the ring homomorphism is local. The main tool for these analyses is a nonlocal version of the amplitude inequality of Iversen, Foxby, and Iyengar. We provide numerous examples demonstrating the need for certain hypotheses and the strictness of many inequalities. 
Anders Frankild and Sean Sather-Wagstaff