Two theorems on excellent rings

Source abstract

Let f : A → B be a homomorphism of commutative noetherian rings. The main results of this paper are: (a) Assume f is finite and induces a surjective map on the spectra. Then if B is quasi-excellent A is quasi-excellent and is excellent if it is universally catenarian (Th. 3.1); and (b) If f is absolutely flat and A is excellent then B is excellent (Th. 5.3). In particular the strict henselization of an excellent local ring is excellent (Cor. 5.6.).