Algebra & Number Theory Seminar | Department Home
Texas Tech University
Title: Gorenstein flat dimensions over local homomorphisms
Abstract: In this talk, we will discuss Gorenstein dimension over local homomorphisms developed by Iyengar and Sather-Wagstaff. For a local homomorphism f: R → S and a homologically finite S-complex X, we show that Gorenstein dimension of X over f equals Gorenstein flat dimension of X over R plus depth of X over R minus depth of X over S. This is analogous to a theorem of Iyengar and Sather-Wagstaff on projective dimension over local homomorphisms. As an application, we improve a known result by removing the assumption that R should have a dualizing complex.